#  @drtrefor Dr. Trefor Bazett Dr. Trefor Bazett posts on YouTube about math, how to, solve, this is the most. They currently have [-------] followers and [---] posts still getting attention that total [------] engagements in the last [--] hours. ### Engagements: [------] [#](/creator/youtube::UC9rTsvTxJnx1DNrDA3Rqa6A/interactions)  - [--] Week [-------] +20% - [--] Month [-------] -23% - [--] Months [----------] +145% - [--] Year [----------] +554% ### Mentions: [--] [#](/creator/youtube::UC9rTsvTxJnx1DNrDA3Rqa6A/posts_active)  - [--] Month [---] -21% - [--] Months [---] +29% - [--] Year [---] +225% ### Followers: [-------] [#](/creator/youtube::UC9rTsvTxJnx1DNrDA3Rqa6A/followers)  - [--] Week [-------] +0.35% - [--] Month [-------] +1.40% - [--] Months [-------] +13% - [--] Year [-------] +23% ### CreatorRank: [-------] [#](/creator/youtube::UC9rTsvTxJnx1DNrDA3Rqa6A/influencer_rank)  ### Social Influence **Social category influence** [finance](/list/finance) 5.26% [technology brands](/list/technology-brands) 2.63% [social networks](/list/social-networks) 1.75% **Social topic influence** [math](/topic/math) #604, [how to](/topic/how-to) 15.79%, [solve](/topic/solve) #779, [this is](/topic/this-is) 9.65%, [space](/topic/space) 8.77%, [education](/topic/education) #4278, [what is](/topic/what-is) 6.14%, [the big](/topic/the-big) #1233, [vector](/topic/vector) 5.26%, [more than](/topic/more-than) 4.39% **Top accounts mentioned or mentioned by** [@overleafeditor](/creator/undefined) [@writefullai](/creator/undefined) [@gametheory](/creator/undefined) ### Top Social Posts Top posts by engagements in the last [--] hours "How to make your LaTeX documents BEAUTIFUL // LaTeX Tutorial Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 In this video we're covering how to make your LaTeX documents BEAUTIFUL. We starts with columns using twocolumn in the document class the multicol package and using minipages. Next up is margins and margin notes. We talk about white space" [YouTube Link](https://youtube.com/watch?v=7B7ytLrMTa0) 2023-04-19T18:23Z 580K followers, 135K engagements "Tables in LaTeX Full Tutorial Intro to LaTeX Episode [--] Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 The file I used in the above video is here: https://www.overleaf.com/read/pjzsxngjqqfp Overleaf's written guide to tables is here: https://www.overleaf.com/learn/latex/Tables This video is all about using tables in LaTeX. I'll show you the basics of the" [YouTube Link](https://youtube.com/watch?v=xyZtxfMsD38) 2022-11-21T17:35Z 580K followers, 148.4K engagements "Intro to VECTOR FIELDS // Sketching by hand & with computers Vector Fields are extremely important in math physics engineering and many other fields. Gravitational fields electric fields magnetic fields velocity fields these are all examples of vector fields. In this video we will define the concept of a vector field talk about some basic terminology practice drawing vector fields by hand and then turn to the technology to plot vector fields on the computer. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa 2D" [YouTube Link](https://youtube.com/watch?v=0QTDisIl9bo) 2020-10-11T15:08Z 580K followers, 159.8K engagements "Proof by Contrapositive Method & First Example Learning objective: prove an implication by showing the contrapositive is true. This video is part of a Discrete Math course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett Mathematics Education University of Cincinnati Discrete Math Proof by Contrapositive Mathematics Education University of Cincinnati Discrete Math Proof by Contrapositive" [YouTube Link](https://youtube.com/watch?v=0YqZIHFmVzg) 2017-06-13T14:46Z 580K followers, 176.2K engagements "The Method of Integrating Factors for Linear 1st Order ODEs **full example** MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs In this video we do a full example using the method of integrating factors to solve a first order differential equation. The first thing to observe is that this is a linear ODE. Then we apply the integral formula to get the integrating factor and finally use that to get a solution to the ODE. ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON:" [YouTube Link](https://youtube.com/watch?v=20x2dNVztlU) 2021-03-01T16:57Z 580K followers, 259K engagements "3D Curves and their Tangents Intro to Vector-Valued Functions A space curve or vector-valued function is a function with a single input t and multiple outputs x(t) y(t) z(t). In this video we introduce these functions and see how to visualize them in 3D. We then turn to the problem of tangent lines to these types of curves. The definition is modeled after tangents to graphs of functions. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems" [YouTube Link](https://youtube.com/watch?v=40r56pX4mqA) 2019-10-08T00:34Z 580K followers, 157.5K engagements "All the LOGARITHMS needed for calculus actually explained Self-study with Brilliant at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription In this video we're going to see all the logarithm rules you should know to take a calculus course. We define logarithm as the inverse function to the exponential so if bx=y then log_b y = x. We really like it when the base is e and this gives the natural logarithm. There are a bunch of rules like for products and quotients and powers but for all of these you can figure out the logarithm" [YouTube Link](https://youtube.com/watch?v=5YoR3b_Wq2w) 2025-02-24T17:41Z 580K followers, 34.2K engagements "Harmonic Series It diverges but insanely slowly After the Geometric Series the Harmonic Series is one of the most important examples in Calculus. This is a series that we will show - by investigating the partial sums - diverges. But it turns out to diverge incredibly slowly taking over [----] terms just to add up to [---]. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=5ejmgwXVSqQ) 2019-02-15T13:44Z 580K followers, 76.5K engagements "Separation of Variables // Differential Equations MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs In this video we talk about our first major method for solving differential equations: the method of separation of variables. A first order ODE is separable if it can be written as y'=f(t)g(y) that is a product of two factors that each only depend on one of the variables. If that is the case then we can separate and integrate. We're going to see in this video the" [YouTube Link](https://youtube.com/watch?v=7Y-frhf-1Zk) 2021-01-27T17:17Z 580K followers, 206.1K engagements "Lagrange Multipliers Geometric Meaning & Full Example Lagrange Multipliers solve constrained optimization problems. That is it is a technique for finding maximum or minimum values of a function subject to some constraint like finding the highest point on a mountain subject to the fact you can only walk along a trail. In this video we study the contour lines or level curves of a function and see geometrically why they are maximized when they are tangent to the constraint curve. That tangency condition leads to the algebraic formula that the gradient of f is equal to lambda times the gradient" [YouTube Link](https://youtube.com/watch?v=8mjcnxGMwFo) 2019-11-27T20:32Z 580K followers, 493.2K engagements "The Multi-Variable Chain Rule: Derivatives of Compositions Suppose that f(xy) depends on two variables but that the x(t) and y(t) are themselves both functions of t. Then f(x(t) y(t)) is a composition of functions and the derivative of f with respect to t is computed via the multi-variable Chain Rule. In fact this scenario is one of many different generalizations of the single variable chain rule. We can use arrow (or dependency) diagrams to illustrate the relationships between a bunch of multivariable functions and for each situation write down a chain rule that gives the slope. The idea in" [YouTube Link](https://youtube.com/watch?v=9yCtWfI_Vjg) 2019-11-13T17:30Z 580K followers, 146.6K engagements "What is VECTOR CALCULUS **Full Course Introduction** MY VECTOR CALCULUS PLAYLIST https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa Welcome to the start of a full course on vector calculus. In this intro video I'm going to give an overview of the major concepts and ideas that we are going to be seeing throughout the course: Vector Fields Line Integrals Surface Integrals Flux & Flow and the big theorems of Green's Theorem Stokes' Theorem and the Divergence Theorem. It's totally ok if everything doesn't click 100% in this first video the goal is to just give the flavour of" [YouTube Link](https://youtube.com/watch?v=AIxiYG-gZ00) 2020-11-29T16:51Z 580K followers, 406K engagements "Undetermined Coefficients: Solving non-homogeneous ODEs MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs How can we solve an ordinary differential equation (ODE) like y''-2y'-3y=3e2t. The problem is the non-homogeneity on the right hand side. If this was homogeneous and just zero then previously in our playlist we've studied how to solve constant coefficient homogeneous equations. To deal with the non-homogeneity we use a method called undetermined coefficients." [YouTube Link](https://youtube.com/watch?v=AgyeJEO2a-k) 2021-04-19T16:10Z 580K followers, 591.5K engagements "What is a DIFFERENTIAL EQUATION **Intro to my full ODE course** Free Open-Source ODE Textbook I'm adapting for this playlist: http://web.uvic.ca/tbazett/diffyqs The ODE Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw In this video I'm giving an introduction to ODEs or Ordinary Differential Equations. Our goal is to model a world where properties are changing and we note from Calculus that rates of change were encoded by the derivative of a function. But where did those functions come from Often the answer is differential equations. We're going to see" [YouTube Link](https://youtube.com/watch?v=B5IjsTONKkw) 2021-01-13T18:13Z 580K followers, 402.8K engagements "Visualizing a 4D Sphere ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=Exl1WQ8sGkg) 2025-11-05T18:26Z 580K followers, 42.2K engagements "Directional Derivatives What's the slope in any direction A directional derivative gives the slope in any particular direction similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient you can get the directional derivative in the u direction with one easy dot" [YouTube Link](https://youtube.com/watch?v=GJODOGq7cAY) 2019-11-17T17:56Z 580K followers, 265.8K engagements "Computing the Fourier Series of EVEN or ODD Functions **full example** In this video we do a full example of computing out a Fourier Series for the case of a sawtooth wave. We get to exploit the fact that this is an odd function where f(-x)=-f(x)) as we can simplify considerably our computations of the Fourier Coefficients if the function is either even or odd. Previous videos in the Fourier Series playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hR Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on" [YouTube Link](https://youtube.com/watch?v=Gs14OvCSxF4) 2021-05-09T15:43Z 580K followers, 201.9K engagements "Defining Double Integration with Riemann Sums Volume under a Surface We generalize the ideas of integration from single-variable calculus to define double integrals. The big idea in single variable calculus was to chop up the region into a sum of little rectangles called the Riemann sum which was an approximation for the area under a function. Then we took a limit of the Riemann sum to define the definite integral. We do much the same here looking to find a formula for the volume under a surface. Now a rectangular region in the domain is broken up into a lot of little prisms and the sum of" [YouTube Link](https://youtube.com/watch?v=JXh9AQkKmsw) 2019-12-01T17:33Z 580K followers, 99.7K engagements "Intro to the Laplace Transform & Three Examples Welcome to a new series on the Laplace Transform. This remarkable tool in mathematics will let us convert differential equations to algebraic equations we can solve and then convert back. In this first video we will define the Laplace Transform as an improper integral. We will see three examples: exponential functions the step function aka Heaviside function and the Laplace Transform of polynomials. The latter examples will make use of something called the Gamma Function and we will see it has nice properties related to factorials. Laplace" [YouTube Link](https://youtube.com/watch?v=KqokoYr_h1A) 2020-03-15T19:37Z 580K followers, 1.3M engagements "Logical Arguments - Modus Ponens & Modus Tollens Modus Ponens and Modus Tollens are two logical argument forms. In either case these have two premises and a conclusion. These argument forms are called valid which means that if you accept the hypotheses then it is valid to conclude the conclusion. This is distinct from having a sound argument which means not only is the structure logically valid but additionally the premises are true. In this video we will learn how to analyze a written argument by its logical structure as well as write out the truth table for Modus Ponens and Modus Tollens." [YouTube Link](https://youtube.com/watch?v=NTSZMdGlo4g) 2017-05-23T00:47Z 580K followers, 469.8K engagements "Analyzing an argument for validity Learning Objectives: 1) Analyze an argument to determine it's logical structure 2) Decide if the logical form of an argument is valid or invalid The main argument forms are Modus Ponens Modus Tollens Generalization Specialization and Contradiction. To see more on each of these check out the following playlist: Full DISCRETE MATH Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Other Course Playlists: CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=ON7yAw6W9VY) 2017-05-23T17:45Z 580K followers, 142.3K engagements "A unified view of Vector Calculus (Stoke's Theorem Divergence Theorem & Green's Theorem) In the final video of my vector calculus playlist (congrats to everyone for making it to the end) I want to do a bit of an overview of the major theorems we have seen in this course - Stokes' Theorem Divergence Theorem Green's Theorem - all are part of a unified framework. Loosely integrating a differential operator such as the curl or divergence along a region equates to a quantity computed just along the boundary. Exactly what quantity (flux vs circulation say) changes depending on the set-up but they" [YouTube Link](https://youtube.com/watch?v=PIoqMNL7tV0) 2020-12-18T16:40Z 580K followers, 155.4K engagements "The Dirac Delta 'Function': How to model an impulse or infinite spike In this introduction to the Dirac Delta Function we'll see how we can deal with something happening instantaneously like a hammer hit. We will model this impulse with a 'function' that is infinite at one point and zero everywhere else. But such a thing isn't really a function Sometimes we called it a functional or a generalized function. Regardless it is defined by its pleasing properties such as what happens when you integrate the dirac delta function multiplied by another function. It can also be thought of as the" [YouTube Link](https://youtube.com/watch?v=SxNVcCVj-3c) 2020-05-09T18:31Z 580K followers, 131.9K engagements "Double Integration in Polar Coordinates Example & Derivation While Cartesian coordinates are great and all some regions and some integrands are way nicer when described using polar coordinates. In this video we play around with polar coordinates derive the formula for double integration in polar coordinates and see an example. The derivation is much like it was in Cartesian coordinates - a limit of a sum of little volumes - but the geometry of the little volumes change in polar coordinates as they no longer have rectangular bases. Full Multivariable Calculus Playlist:" [YouTube Link](https://youtube.com/watch?v=U-13q74uvTo) 2019-12-08T20:14Z 580K followers, 173.3K engagements "Torsion: How curves twist in space and the TNB or Frenet Frame If you have a curve through space torsion measures the degree to which the curve "twists". This is separate from how the curve "curves" which we saw was given by the curvature formula. In this video we will study the TNB or Frenet Frame given by three vectors the Tangent the principle Normal and the new vector called the BiNormal vector. The Tangent and Normal Vectors define a plane and what Torsion measures is how that plane changes as you move along the curve. TYPO: Near the beginning the Normal Vector should be 1/k dT/ds. I" [YouTube Link](https://youtube.com/watch?v=VIqA8U9ozIA) 2019-10-23T19:54Z 580K followers, 198.8K engagements "Bayes' Theorem - The Simplest Case Second Bayes' Theorem example: https://www.youtube.com/watchv=k6Dw0on6NtM Third Bayes' Theorem example: https://www.youtube.com/watchv=HaYbxQC61pw FULL Discrete Math Playlist: https://www.youtube.com/watchv=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(AB) to P(BA). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given" [YouTube Link](https://youtube.com/watch?v=XQoLVl31ZfQ) 2017-11-19T01:32Z 580K followers, 1.9M engagements "Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Consider a mass on a spring moving horizontally. The only force on the mass is the spring itself which we can model using Hooke's Law. Then by Newton's Second Law that F=ma this gives the differential equation mx''+kx=0. This is a second order constant coefficient homogeneous differential equation which we can study We use our techniques from" [YouTube Link](https://youtube.com/watch?v=Z52emur7Rko) 2021-04-11T16:10Z 580K followers, 101.3K engagements "Multi-variable Optimization & the Second Derivative Test Finding Maximums and Minimums of multi-variable functions works pretty similar to single variable functions. Firstfind candidates for maximums/minimums by finding critical points. Critical Points are where the partial derivatives with respect to x and y are both zero. Then we classify each critical point using the second derivative test. In the multivariable case there is a new option beyond max/min/neither there is also the case of the saddle point. The second derivative test involves computing the Hessian the determinant of a matrix" [YouTube Link](https://youtube.com/watch?v=_Ffcr98c7EE) 2019-11-24T17:40Z 580K followers, 143.8K engagements "Unlocking the secrets of Magic Square puzzles Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription Magic Square puzzles are some of my favourite recreational math puzzles. Fill up a 3x3 square with the numbers [--] through [--] each used once so every row column and main diagonals add up to the same number. More generally it can be a nxn square with numbers [--] through n2 and there are actually tonnes of variants of these. In this video we will prove that there is precisely [--] possible 3x3 magic" [YouTube Link](https://youtube.com/watch?v=fb2rvckCR8M) 2023-05-30T15:45Z 580K followers, 70.3K engagements "Using Laplace Transforms to solve Differential Equations ***full example*** How can we use the Laplace Transform to solve an Initial Value Problem (IVP) consisting of an ODE together with initial conditions in this video we do a full walkthrough beginning with the differential equation converting it to an algebraic equation via the Laplace Transform solving that algebraic equation and finally converting back to a solution to the IVP through the Inverse Laplace Transform. This is part of my series on the Laplace Transforms in my Differential Equations Playlist:" [YouTube Link](https://youtube.com/watch?v=fuxFrpaMLtw) 2020-03-21T23:40Z 580K followers, 380.5K engagements "What does "equal" actually mean Get better at MATH and Computer Science with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:" [YouTube Link](https://youtube.com/watch?v=iNdHFP75PpA) 2025-12-01T18:03Z 580K followers, 83K engagements "Intro to Conditional Probability What is the probability of an event A given that event B has occurred We call this conditional probability and it is governed by the formula that P(AB) which reads "probability of A given B" is equal to the P(A intersect B)/P(B). We look at an example involving the probability of being an alcoholic given that one is a man. Conditional Probability Formula: P(AB) = P(A and B)/P(B) FULL DISCRETE MATH PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH" [YouTube Link](https://youtube.com/watch?v=ibINrxJLvlM) 2017-11-19T00:46Z 580K followers, 1.6M engagements "How to Compute a FOURIER SERIES // Formulas & Full Example How do you actually compute a Fourier Series In this video I walk through all the big formulas needed to compute the coefficients in a Fourier Series. First we see three integrals that will really make everything easier integrals of products of sin and cos terms of different frequencies. Then we will use these to compute out formulas for the coefficients of the in and cos terms. Next we see a full example computing everything and finally see the formulas for the general situation. Watch the first video in my playlist here:" [YouTube Link](https://youtube.com/watch?v=ijQaTAT3kOg) 2021-05-06T15:39Z 580K followers, 532.2K engagements "Finding the scalar potential function for a conservative vector field // Vector Calculus The fundamental theorem of line integrals told us that if we knew a vector field was conservative and thus able to be written as the gradient of a scalar potential function we could evaluate any line integral almost trivially by just evaluating that potential function at the endpoints. But how do we FIND the scalar potential function This video introduces that method. First we test that our vector field really is conservative using the test we saw previously. But after we know the method applies we apply" [YouTube Link](https://youtube.com/watch?v=jlza4rEFXKM) 2020-11-16T17:12Z 580K followers, 166K engagements "Rotation Matrices Linear Algebra Fundamentals Get better at MATH and Computer Science with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription FULL PLAYLIST: LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett 0:00 Rotations" [YouTube Link](https://youtube.com/watch?v=rUKsjo1nReE) 2025-11-17T18:43Z 580K followers, 14.1K engagements "Flux Integrals // Big Idea Formula & Examples // Vector Calculus The Flux along a closed curve measures the degree to which a vector field is crossing outward across the curve. We compute this using a flux integral. In contrast to our previous video discussing flow which represented the degree to which the field was tangential to the curve flux accumulates the degree to which the field is normal to the curve. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa 0:00 Geometric Idea 2:15 Formula 4:40 Derivation 9:06" [YouTube Link](https://youtube.com/watch?v=sX9s0JiWATM) 2020-10-28T16:27Z 580K followers, 125.5K engagements "Change of Variables & The Jacobian Multi-variable Integration You've reached the end of Multi-variable Calculus In this video we generalized the good old "u-subs" of first year calculus to multivariable case with a multivariable change of variables. The trick is to set up a new coordinate system where the messy region before is now very nice perhaps just a rectangle. We have to be careful though as we have to multiply our integrands by a scaling factors called the Jacobian. In this video I sketch the intuition behind the Jacobian and compute it out in an example." [YouTube Link](https://youtube.com/watch?v=wUF-lyyWpUc) 2019-12-18T20:53Z 580K followers, 421.6K engagements "The Laplace Transform of Derivatives and Integrals In this video we take the Laplace Transform of derivatives or integrals. What's amazing is that these result in expressions entirely in terms of the original function. This will be important for us when we take the Laplace Transform of a differential equation because it will convert an ODE with initial conditions into an algebraic equation we can hopefully solve more easily. Formulas: 1) Lf(t)=sF(s)-f(0) 2)L integral from [--] to t of f(tau) = F(s)/s This is part of my series on the Laplace Transforms in my Differential Equations Playlist:" [YouTube Link](https://youtube.com/watch?v=zfhyeXbb0d4) 2020-03-18T21:11Z 580K followers, 193.8K engagements "Line Integrals of Vector Fields // Big Idea Definition & Formula Previously in the Vector Calculus playlist (see below) we have seen the idea of a Line Integral which was an accumulation of some function along a curve. In this video we're going to look at case where we begin with a vector field and want to measure the accumulation of the field tangential to the curve. A great example of this is the physics concept of work done by a field on a particle moving along a curve. In this video we will define the basic concept of the line integral of a vector field along a curve and then determine a" [YouTube Link](https://youtube.com/watch?v=059LjQ2oLBM) 2020-10-14T15:00Z 578K followers, 244.4K engagements "The beautiful geometric view of FOURIER SERIES // The Linear Algebra Perspective Fourier Series can sometimes seem very computational and full of integrals but there is actually a very deep and important geometric picture that is analogous to Linear Algebra. So many core ideas from linear algebra like bases linear independence orthogonality inner products and projections all have their analogs in Fourier Series. Effectively the idea of computing a Fourier Series is just decomposing a vector in an orthonormal basis. Cool The rest of my Fourier Series Playlist:" [YouTube Link](https://youtube.com/watch?v=1Ez1tn1mei8) 2021-05-12T15:47Z 579K followers, 80.5K engagements "Subspaces of Rn Subspaces are those subsets that play nice with the fundamental operations on vectors. That is we say they are "closed under scalar multiplication" and "closed under vector addiction". Examples include everything just the zero vector and lines through the origin. Learning Objectives 1) Define a subspace 2) Determine if a set is a subspace by checking whether it satisfies the three properties. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS &" [YouTube Link](https://youtube.com/watch?v=5EzOI8PL3DI) 2017-06-11T00:30Z 580K followers, 15.3K engagements "Vector Spaces Definition & Examples Vectors in Rn obey a list of rules things like commutivity of vector addition that a+b = b+a as vectors. However we can abstract this list of rules and introduce the general concept of a vector space. A vector space has elements that might be all kinds of weird things but as long as they obey the same list of rules they are a vector space. And the key here is that all the things we have done in linear algebra extend to this new situation too Our first new example is polynomial of degree less than or equal [--] which have a natural "vector" addition and scalar" [YouTube Link](https://youtube.com/watch?v=72GtkP6nP_A) 2018-06-16T20:27Z 580K followers, 128.9K engagements "Divergence Flux and Green's Theorem // Vector Calculus In the previous video in our Vector Calculus Playlist (https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa) we saw Part I of Green's Theorem which related the local property of Curl (aka circulation density) with the global property of Circulation. Circulation a line integral over a vector field was compared to a double integral over the area enclosed of the Flux. In this video we look at Part II of Green's Theorem which now contrasts the local property of Divergence (aka Flux Density) with the global property of" [YouTube Link](https://youtube.com/watch?v=GsjJs71SBec) 2020-11-18T16:28Z 579K followers, 105.9K engagements "The Illusion of Thinking // The new Apple AI paper is.something Get better at MATH with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription Check out: 1) The main Apple paper (and source of all graphs from the video): https://ml-site.cdn-apple.com/papers/the-illusion-of-thinking.pdf 2) Play the Towers of Hanoi game here: https://www.mathsisfun.com/games/towerofhanoi.html ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25%" [YouTube Link](https://youtube.com/watch?v=H3YvlRBEx1I) 2025-06-11T16:45Z 580K followers, 55.5K engagements "Stirling's Incredible Approximation // Gamma Functions Gaussians and Laplace's Method We prove Stirling's Formula that approximates n using Laplace's Method. Get my favorite free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Check out MAPLE LEARN for your browser to make beautiful graphs and much more: https://www.maplesoft.com/products/learn/p=TC-9857 Check out Maplesoft's YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ In his video we prove Stirling's Approximation Formula that n" [YouTube Link](https://youtube.com/watch?v=JsUI40uSOTU) 2021-11-02T16:34Z 579K followers, 150K engagements "Normal Form Games // Intro to Game Theory // Episode [--] Check out Brilliant https://brilliant.org/TreforBazett/ Join for free and the first [---] subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video The 1st episode in the Game Theory playlist on the Prisoners Dilemma: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX In this video we introduce our first major category of game that we will study in Game Theory called Normal Form Games. These are games between a finite number of players with each player having a finite" [YouTube Link](https://youtube.com/watch?v=TVlf43FmuPY) 2021-07-14T16:19Z 578K followers, 19.5K engagements "Example: Writing a vector in a new basis Let's work through an explicit example using the change of basis formula from the previous video. Learning Objectives: 1) Given two basis convert a vector expressed in one basis to the other. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett Mathematics Education University of Cincinnati Linear Algebra Change of Basis Mathematics Education" [YouTube Link](https://youtube.com/watch?v=TZPZczNzNN4) 2017-06-24T18:46Z 580K followers, 20.2K engagements "What is a LINE INTEGRAL // Big Idea Derivation & Formula My Vector Calculus playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa A line integral - sometimes called a path integral - is an accumulation of something along a curve (again sometimes called a path). In this first video we will really focus on a curve living in 2D with a height above that curve and answer the question of what is the surface area that results This will be four first major application of line integrals. The plan for this video is to introduce the big idea of line integrals come up with a" [YouTube Link](https://youtube.com/watch?v=WA5_a3C2iqY) 2020-09-21T16:22Z 580K followers, 352.8K engagements "Power Series & Intervals of Convergence Power series are series of the form c_n (x-a)n where the c_n is a sequence and x is thought of as a variable. Whether it converges or diverges depends on the x. By applying the Ratio Test we decide the interval upon which the Power Series converges as well as the "ratio of convergence" and the "center" of the power series. The results turn out very analogous to Geometric Series. Full Course Playlist: CALCULUS II: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON:" [YouTube Link](https://youtube.com/watch?v=XHoRBh4hQNU) 2019-02-28T12:25Z 579K followers, 167.1K engagements "Intro to Kolmogorov Complexity Typo 1: 25=32 not [--] Just pretend I said "32" throughout the entire video:D Oops. Typo 2: More importantly is that I missed the on the length when talking about randomness at 4:19 and 15:46. That is we say a string y is kolmogorov random aka incompressible if K(y) is greater than or equal to y not just y as written. Kolmogorov Complexity is loosely the shortest computer program that outputs a given string. We'll use this to define a notation of being Kolmogorov random (aka incompressible) and use that to come up with a very nice proof that there are infinitely" [YouTube Link](https://youtube.com/watch?v=baf_iPT7lqI) 2025-02-09T17:28Z 580K followers, 42.3K engagements "Inverse Laplace Transform Example using Partial Fractions In this video in my series on Laplace Transforms we practice compute Inverse Laplace Transforms. In this specific example the rational function isn't of the form where we can use Inverse Laplace Transforms directly so we use Partial Fractions to decompose it into a more straight forward format. Specially this Partial Fraction Decomposition involves repeated linear factors. Finally we use the Laplace Transform table of known functions together with the translation property to compute the final answer. This is part of my series on the" [YouTube Link](https://youtube.com/watch?v=c6YnYr8KsSo) 2020-04-05T19:29Z 578K followers, 202.3K engagements "Euler Paths & the [--] Bridges of Konigsberg Graph Theory An Euler Path walks through a graph going from vertex to vertex hitting each edge exactly once. But only some types of graphs have these Euler Paths it depends on the degree of the vertices. We state and motivate the big theorem and then use it to solve the infamous [--] bridges of Konigsberg problem that motivated Euler to start studying graph theory. FULL DISCRETE MATH PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS OTHER COURSE PLAYLISTS: CALCULUS I:" [YouTube Link](https://youtube.com/watch?v=dSK5jTEe-AM) 2018-12-06T14:34Z 578K followers, 64.3K engagements "Absolute Convergence vs Conditional Convergence vs Convergence We've seen regular convergence of a series before but now we consider two special cases. Absolute convergence is when we take the series of the absolute value of the terms which gets rid of any possible cancellation like what happened a lot in the Alternating Series Test. Absolute convergence implies regular convergence. Conditional Convergence is when it converges but does not converge absolutely. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you" [YouTube Link](https://youtube.com/watch?v=k6AovDCSY8A) 2019-02-22T12:20Z 579K followers, 50.3K engagements "Did I make a 4D bubble Check out the full length video: https://www.youtube.com/watchv=_ex1z7XBA_M ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE trefor25 for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I:" [YouTube Link](https://youtube.com/watch?v=m8cav0cF5yM) 2025-08-04T19:47Z 580K followers, 3.3M engagements "Deriving the Change-of-Basis formula Description: If I have a vector expressed in one basis we can compute what that vector is expressed in a different basis via the formula derived in this video. Learning Objectives: 1) Write a vector (given in the standard basis) as a matrix times the vector written in a new basis. 2) Write a vector (given in this new basis) as the inverted matrix times the vector written in the standard basis 3) Given a vector in one basis write the vector in some other basis. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A" [YouTube Link](https://youtube.com/watch?v=njvTyIWtxrE) 2017-06-24T00:10Z 579K followers, [----] engagements "Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs While we saw a specific example of Constant Coefficient Homogeneous ODEs in my previous video in the playlist in this video we're going to solve it in generality and really elaborate on the three main cases. The characteristic equation aka auxiliary equation can have either real and distinct root real and repeated roots or complex" [YouTube Link](https://youtube.com/watch?v=r8Uk4tbuxVE) 2021-03-24T16:09Z 578K followers, 103.2K engagements "Strong Induction // Intro and Full Example Strong Induction is a proof method that is a somewhat more general form of normal induction that let's us widen the set of claims we can prove. Our base case is not a single fact but a list of all the facts up to a particular nth level. Then we demonstrate the (n+1)th level. Previous example: Induction Proofs with inequalities: https://www.youtube.com/watchv=L5iCGi3dW-Y Full DISCRETE MATH Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor" [YouTube Link](https://youtube.com/watch?v=rfA0h9udl7E) 2017-06-19T21:58Z 580K followers, 296.8K engagements "Intro to FOURIER SERIES: The Big Idea Welcome to my playlist on Fourier Series. In this first video we explore the big idea of taking a periodic function and approximating it with sin and cos terms of various frequencies. We will define Fourier Series and see what it means for the series to converge to the original function. We'll also see a bit about Gibbs phenomena and what happens around discontinuities. Rest of the videos in this playlist are here: https://www.youtube.com/watchv=wmCIrpLBFds&list=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hR&ab_channel=Dr.TreforBazett ♡♡♡SUPPORT THE CHANNEL♡♡♡" [YouTube Link](https://youtube.com/watch?v=wmCIrpLBFds) 2021-05-03T15:50Z 578K followers, 402.5K engagements "How to solve ODEs with infinite series Intro & Easiest Example: y'=y In this video we see how to find series solutions to solve ordinary differential equations. This is an incredibly powerful tool that really expands the amount of differential equations we can solve. We will first introduce power series and their basic principles along with the standard series expandions for sin(x) cos(x) ex and 1/(1-x) the geometric series. We'll then see how to substitute the series solution into the differential equation manipulate indices and get a recurrence relation on the coefficients. By studying this" [YouTube Link](https://youtube.com/watch?v=xeeM3TT4Zgg) 2020-05-26T16:49Z 578K followers, 102.8K engagements "Why hyperbolic functions are actually really nice Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription Today we unpack everything to do with hyperbolic functions. In calculus we often see an analytic definition of hyperbolic cosine and hyperbolic sin expressed as exponential functions. But why Analytically this is just asking for the even and odd components of ex. However we can connect this geometrically to hyperbolas and specifically to the area enclosed by a hyperbola. ♡♡♡SUPPORT THE" [YouTube Link](https://youtube.com/watch?v=HnHnEnkZpJA) 2023-10-30T17:22Z 580K followers, 291K engagements "Flux of a Vector Field Across a Surface // Vector Calculus in his video we derive the formula for the flux of a vector field across a surface. This is very analogous to our two dimensional story about the flux across a curve. We can describe surfaces either parametrically explicitly or implicitly and so we come up with formula for the flux across a surface for each description. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: DISCRETE MATH:" [YouTube Link](https://youtube.com/watch?v=eYhUm2KJnM4) 2020-12-08T16:52Z 580K followers, 88.9K engagements "Conservative Vector Fields // Vector Calculus Many vector fields - such as the gravitational field - have a remarkable property called being a conservative vector field which means that line integrals over that field are path independent. That is if you want to compute a line integral (physically interpreted as work) the ONLY thing that matters is the endpoints not what happens along the field. Cool In this video we define the basic idea and compute out an example modelling gravity that shows this is a conservative vector field. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV)" [YouTube Link](https://youtube.com/watch?v=76nzOtupeRc) 2020-11-03T17:42Z 580K followers, 146K engagements "The Null Space & Column Space of a Matrix Algebraically & Geometrically To every matrix there are two natural subspaces: the Null Space of A and the Column Space of A denoted Null(A) and Col(A). Col(A) is the range or all the vectors "hit" by a transformation. It turns out this is equivalent to the span of the columns of A. Null(A) is all the vectors in the domain that are sent to zero by the transformation. We visualize these two subspaces prove they actually are subspaces and show how to compute them. ************************************************** Now it's your turn: 1) Summarize the" [YouTube Link](https://youtube.com/watch?v=YQRioQ1XUck) 2018-06-16T19:27Z 580K followers, 104.2K engagements "The Bernoulli Equation // Substitutions in Differential Equations MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs The Bernoulli Equation is a fascinating ODE. On the surface it is a non-linear first order ODE which means we can't use the methods we have developed for first order linear differential equations. However with a substitution u=y(1-n) this converts into a linear ODE and then we can use the method of integrating factors. There are a lot of little" [YouTube Link](https://youtube.com/watch?v=iCN8nGXE29o) 2021-03-08T15:49Z 580K followers, 235K engagements "What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( // Banach Fixed Point Theorem This weird expression of taking cos over and over again is just a sequence x_n=cos(x_n-1). There is a very cool theorem called the Banach Fixed Point Theorem that let's figure out the limit of sequences like this and depends on cos(x) being a so called contractible mapping. 0:00 The sequence 1:17 Cos(x) Graphically 3:25 Spiral Geometric View 7:02 Banach Fixed Point Theorem COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:" [YouTube Link](https://youtube.com/watch?v=qHnXE_h5c2M) 2022-01-10T17:07Z 580K followers, 749.3K engagements "The Dimension Theorem Dim(Null(A)) + Dim(Col(A)) = n Also Rank The two canonical subspace of a matrix - the null space and the column space - may seem very different. The null space is in the domain the column space is in the codomain for instance. But they are related by the Dimension Theorem This says that Dim(Null(A)) + Dim(Col(A)) = n. We're going to investigate why this is the case algebraically and geometrically. Along the way we define a new invariant called rank which is just a convenient way to say the number of leading 1s in REF form." [YouTube Link](https://youtube.com/watch?v=vpl8EZwrqPk) 2018-06-24T13:07Z 580K followers, 47.2K engagements "How to find the TANGENT PLANE Linear approximation of multi-variable functions How do you find the equation of a tangent plane to the graph of a function f(xy) This is the multi-variable analog of finding the equation of a tangent line to the single variable function f(x). At each point (if f is differentiable) the tangent plane is a linear approximation. To compute this we use the vector equation of a plane with respect to the normal vector. The components of the normal vector come from the partial derivatives so if you can find partial derivatives you can write down the equation of the" [YouTube Link](https://youtube.com/watch?v=wqtr4Udz8AY) 2019-11-20T01:36Z 580K followers, 189.1K engagements "9 tips to help you PROVE MATH THEOREMS How can you prove math theorems How do you begin What are the types of logical arguments you can use How do you get unstuck when you don't know what to do In this video i'm going to walk through a series of tips and tricks to help you prove mathematical theorems. We'll talk about the logical structure and contrast proof methods like direct contrapositive contradiction and counterexample. I'll give you concrete template to work from assumptions definitions of assumptions manipulations definition of conclusion and finally the conclusion. And then i'll talk" [YouTube Link](https://youtube.com/watch?v=-6b-tQEBUT8) 2020-07-05T18:50Z 580K followers, 162K engagements "Intro to LaTeX **Full Tutorial** Part II (Equations Tables Figures Theorems Macros and more) Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Part I of my tutorial on LaTeX is here: https://www.youtube.com/watchv=Jp0lPj2-DQA The rest of my LaTeX playlist is here: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link):" [YouTube Link](https://youtube.com/watch?v=-HvRvBjBAvg) 2021-08-10T16:06Z 580K followers, 305.9K engagements "Cantor's Diagonal Argument: The rationals and reals have different sizes Cool Math Episode 1: https://www.youtube.com/watchv=WQWkG9cQ8NQ In the first episode we saw that the integers and rationals (numbers like 3/5) have the same "size" - that is there is a bijective function so that you can line up the integers and rationals even though they are infinite sets and even though the rationals has elements like 3/5 that aren't in the integers. In this episode we now compare the integers and the REAL numbers. Using Cantor's Diagonalization Argument we attempt to list all the real numbers - that is" [YouTube Link](https://youtube.com/watch?v=0HF39OWyl54) 2018-04-10T15:37Z 580K followers, 118.9K engagements "Relations between two sets Definition + First Examples Learning Objectives: 1) Recognize "less than" as an example of a relation 2) Draw a visual picture of a relation 3) State the formal definition of a relation **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS" [YouTube Link](https://youtube.com/watch?v=0dzNlrNJYdc) 2017-05-05T04:14Z 580K followers, 149.3K engagements "The Mobius Strip Bubble ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=0pWW0maO3jA) 2025-09-07T15:27Z 580K followers, 253.3K engagements "Choosing Which Convergence Test to Apply to [--] Series Deciding which convergence test to apply to a given series is often the hardest part of the unit on series convergence. In this video I'm going to loosely walk through some larger strategies for picking and choosing the method focusing on [--] different series and [--] different methods: 0:00 Intro 0:38 Geometric Series 1:30 Integral Test 2:52 Alternating Series Test 3:54 Divergence Test 5:08 Comparison Test 6:46 Limit Comparison Test 7:58 Root Test 8:52 Ratio Test ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH" [YouTube Link](https://youtube.com/watch?v=0wefqjpQyKM) 2019-02-25T12:31Z 580K followers, 655.9K engagements "My favorite LaTeX packages for writing beautiful math documents Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out my LaTeX playlist from complete beginner to expert: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 Check out the specific Overleaf document from this video: https://www.overleaf.com/read/cmprhhrbxrgv#0368fe 0:00 Intro to LaTeX 1:15 Sharing in Overleaf 2:20 Links and urls with hyperref 6:06 Code and quotes with fancyvrb 8:40 Headers" [YouTube Link](https://youtube.com/watch?v=331YxgOJUGw) 2021-11-16T17:31Z 580K followers, 240.1K engagements "How I make beautiful GRAPHS and PLOTS using LaTeX Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 I make most of my graph and plots inside of LaTeX using a package called pgfplots. LaTeX is a type setting language and I like using it for graphs specifically because I can control all aspects of my graphs very precisely with formatting native and easily" [YouTube Link](https://youtube.com/watch?v=5jmIHOWpEg0) 2022-05-30T16:35Z 580K followers, 584.4K engagements "Continuity vs Partial Derivatives vs Differentiability My Favorite Multivariable Function In single variable calculus a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus you might expect a similar relationship with partial derivatives and continuity but it turns out this is not the case In this example what I call the cross function we will see that both partial derivatives exist but that the function is nonetheless not continuous. This means our work is still cut out for us: we need to define a" [YouTube Link](https://youtube.com/watch?v=6Wi1kT9kR1M) 2020-06-14T17:31Z 580K followers, 91.7K engagements "3 Ways to Show a Logical Equivalence Ex: DeMorgan's Laws DeMorgan's Laws are two important logical equivalences. In introducing these laws I talk about three different ways by which you can demonstrate a logical equivalences: There are truth tables citing known laws and testing for reasonableness. Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett CURIOSITY BOX:" [YouTube Link](https://youtube.com/watch?v=93CxSLi89Ok) 2019-01-23T12:55Z 580K followers, 240.9K engagements "The Key Definitions of Differential Equations: ODE order solution initial condition IVP Get the free Maple Calculator for your phonehttps://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Get Maple Learn for your computer https://www.maplesoft.com/products/learn/p=TC-9857 The Differential Equations playlist https://www.youtube.com/watchv=B5IjsTONKkw&list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw&ab_channel=Dr.TreforBazett Free Open Source textbook on ODEs http://web.uvic.ca/tbazett/diffyqs/ In this video I introduce the core concepts and the precise definitions of Differential" [YouTube Link](https://youtube.com/watch?v=C3WKwB5gBqI) 2021-01-20T18:10Z 580K followers, 147.2K engagements "The Gradient Vector Field One prominent example of a vector field is the Gradient Vector Field. Given any scalar multivariable function f: Rnto R we can get a corresponding vector field that has a precise geometrical meaning: the vectors point in the direction of maximal increase of the function. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:" [YouTube Link](https://youtube.com/watch?v=DG9NUPaPVbE) 2020-10-11T15:09Z 580K followers, 166.8K engagements "Dirac's Belt Trick: Why a [--] rotation twists space but a [--] rotation fixes it Visit https://brilliant.org/TreforBazett/ to help you learn STEM topics for free and the first [---] people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations https://www.beautifulequation.com/pages/trefor When you twist your arm or a belt by [---] degrees the hand or endpoint is back to where it started but the rest of your arm or belt is still twisted. But if you do a [---] degree twist you can manage to untwist your arm or belt This is known as Dirac's" [YouTube Link](https://youtube.com/watch?v=EgsUDby0X1M) 2022-05-23T15:03Z 580K followers, 74.4K engagements "Conditional Statements: if p then q Learning Objectives: 1) Interpret sentences as being conditional statements 2) Write the truth table for a conditional in its implication form 3) Use truth tables to see the disjunctive form of a conditional statement as logically equivalent Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use" [YouTube Link](https://youtube.com/watch?v=F3544ZyO-eU) 2017-05-17T22:33Z 580K followers, 936.5K engagements "The best way to stack blocks ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=FYgrDtFyNt4) 2025-10-05T17:47Z 580K followers, 355K engagements "Geometric Series Convergence Derivation and Example The Geometric Series is one of our foundational series. Unlike most series we will se in Calculus where we can determine convergence but not what it actually converges too for the Geometric Series in fact we not only know exactly when it converges but also what it converges too. Full Course Playlist: CALCULUS II: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett" [YouTube Link](https://youtube.com/watch?v=Gs1Qc8XKtqM) 2019-02-14T12:42Z 580K followers, 168.8K engagements "What is a Solution to a Linear System **Intro** We kick off our course by establishing the core problem of Linear Algebra. This video introduces the algebraic side of Linear Systems (the next will address the geometric side). In particular we will be able to: *Identify when an equation is linear *Define what a system of linear equations is *Verify that a list of values is a solution to a system of linear equations *Use a_ij notation to express generic linear systems *Use the terminology of coefficients constants and variables. Now it's your turn: 1) Summarize the big idea of this video in" [YouTube Link](https://youtube.com/watch?v=H8MiZMJr1kQ) 2018-04-28T18:03Z 580K followers, 123.6K engagements "Equations of Planes: Vector & Component Forms Multivariable Calculus We will come up with first the vector form of the equation of a plane and then expand to get the component form of the equation of a plane. The formula is based on knowing: 1) A point on the plane 2) A normal vector to the plane Planes are foundational objects in multivariable calculus (for instance the analog of a tangent line for functions of one variable will be a tangent plane for functions in two variable). Full Multivariable Calculus Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd" [YouTube Link](https://youtube.com/watch?v=HjJ140TYbXQ) 2019-08-25T16:08Z 580K followers, 188.4K engagements "An infinite block overhang ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:" [YouTube Link](https://youtube.com/watch?v=HlXM4cNJsxc) 2025-09-30T16:14Z 580K followers, 6.6M engagements "Intro to Linear Programming This optimization technique is so cool Get Maple Learn https://www.maplesoft.com/products/learn/p=TC-9857 Get the free Maple Calculator for your phonehttps://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Play around with the exact Maple Learn document I use in the video https://learn.maplesoft.com/#/docId=5586126131167232&key=4B4CFF82514F4F57AC213F59E24CB275B7F3DB27B846486D9CDA0555BD8423CD Play around with the Maple Learn document I use in the video" [YouTube Link](https://youtube.com/watch?v=K7TL5NMlKIk) 2021-04-06T15:55Z 580K followers, 302.9K engagements "Change the order of integration to solve tricky integrals The double integral over a region can be expressed in two different ways. It could be that we write dxdy which means that we integrate with respect to x first and then y (called horizontal strip). Or it could be dydx which means y is integrated first and then x (vertical strips). The big idea is we can convert between these and so can choose whichever is the easier of the two. The steps are: 1) Given an integral sketch the region implied by the limits of integration 2) Now interpret that region the opposite way such as vertical strips" [YouTube Link](https://youtube.com/watch?v=LUvynduoUX0) 2020-07-22T15:48Z 580K followers, 289.8K engagements "Lagrange Multipliers with TWO constraints Multivariable Optimization In our introduction to Lagrange Multipliers we looked at the geometric meaning and saw an example when our goal was to optimize a function (i.e. find maximums and minimums) subject to ONE constraint:https://www.youtube.com/watchv=8mjcnxGMwFo Now we are upgrading to the case of optimizing with two constraints. We will look at how to interpret the lagrange multiplier method geometrically for two constrains and then see a full example. We will also look at the geometry of the special case of optimization function: the distance." [YouTube Link](https://youtube.com/watch?v=LeKXDMtXBFw) 2020-06-28T18:34Z 580K followers, 94.6K engagements "Geometric Meaning of the Gradient Vector What direction should you travel to increase your height on a mountain as fast as possible What direction should you travel to keep your height constant (i.e. travel on a contour aka a level curve) In this video we discuss the math of this problem assuming we had some nice function describing the height of the mountain. The gradiant vector whose components are the respective partial derivatives gives us the answer to the direction of maximal increase. Indeed we saw previously how directional derivatives could be written in terms of the gradient vector." [YouTube Link](https://youtube.com/watch?v=QQPz3eXXgQI) 2020-06-21T15:45Z 580K followers, 282.9K engagements "How I use AI in LaTeX -- my favorite workflow with Overleaf & Writefull Get started with LaTeX with Overleaf https://www.overleaf.com/registerutm_source=trefor_bazett&utm_medium=youtube&utm_campaign=ol_wf_dec_2022 The AI integrations in this video are made possible due to a collaboration between @overleafeditor and @writefull_ai . My thanks to Overleaf & Writefull for sponsoring today's video FULL LaTeX Playlist https://www.youtube.com/watchv=Jp0lPj2-DQA&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&ab_channel=Dr.TreforBazett 0:00 Intro 1:35 Getting started with LaTeX 3:00 Equations 5:03 Formatting" [YouTube Link](https://youtube.com/watch?v=T_dAb3vTx4U) 2024-12-02T16:31Z 580K followers, 72.6K engagements "The Theory of 2nd Order ODEs // Existence & Uniqueness Superposition & Linear Independence MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Previously in our ODE playlist we've studied 1st order differential equations. Now we move to second order differential equations and specifically focus at the beginning on the major theory. What does existence and uniqueness look like for 2nd order linear ODEs We see a remarkable property called superposition and finally we" [YouTube Link](https://youtube.com/watch?v=VpZOuOJ_ob4) 2021-03-18T15:31Z 580K followers, 95K engagements "What's the big idea of Linear Algebra **Course Intro** This is the start of a one semester university level course on Linear Algebra that emphasizes both conceptual understanding as well as procedural fluency with the techniques of Linear Algebra. In this video we get to see just the beginning of some of the big ideas of Linear Algebra. FULL PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 Linear Algebra is a story told in two worlds one geometric and one algebraic. The interplay between the two is beautiful and powerful. In this video we introduce the notion" [YouTube Link](https://youtube.com/watch?v=ZKUqtErZCiU) 2018-02-18T17:24Z 580K followers, 510.4K engagements "The Big Theorem of Differential Equations: Existence & Uniqueness MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs The theory of differential equations works because of a class of theorems called existence and uniqueness theorems. They tell us given an initial value problem when that IVP has a solution and if a solution exists then it also tells us it is unique. We will focus on the Picard or Picard-Lindelof existence and uniqueness theorem which applies to first" [YouTube Link](https://youtube.com/watch?v=_WpncZ3RkTg) 2021-02-21T16:33Z 580K followers, 308.8K engagements "Set-Roster vs Set-Builder notation Learning Objectives: 1) Write a set with infinitely many elements using Set-Roster notation 2) Write a set using Set-Builder notation 3) Convert between these two different notations for sets. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS" [YouTube Link](https://youtube.com/watch?v=aTlR03t1dTQ) 2017-04-25T03:17Z 580K followers, 183.2K engagements "How to write your homework using LaTeX Get the (free) Homework Template https://www.overleaf.com/read/pycnqvvptsvf#94a8a3. This template is on Overleaf my thanks to Overleaf for sponsoring today's video. Overleaf is a cloud-based LaTeX editor that makes it particularly easy (and free) to get started learning LaTeX. The LaTeX full playlist https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 0:00 Intro to LaTeX 1:14 Getting started using Overleaf 2:00 Changing the header 2:58 Basic equations 5:00 Making new problems 7:39 Tables 10:35 Matrices 11:15 Graphics 12:47 Aligned" [YouTube Link](https://youtube.com/watch?v=cI0gGcYOkiI) 2023-12-05T18:30Z 580K followers, 148K engagements "All the TRIG you need for calculus actually explained Get better at trig and so much more math at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription This video is all about trigonometry focusing on reviewing everything you are likely to actually use regularly in calculus. Instead of having to memorize a million trig identities I want to show how you can understand trig where the formulas come from and how you can figure them out on your own if you randomly need one in the middle of a test. ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support" [YouTube Link](https://youtube.com/watch?v=e7QjCL7lQM4) 2024-09-11T16:07Z 580K followers, 387K engagements "Intro to Gradient Descent Optimizing High-Dimensional Equations Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription How can we find maximums and minimums for complicated functions with an enormous number of variables like you might get when studying neural networks or machine learning In this video we are going to talk about a topic from nonlinear optimization called Gradient Descent (or Gradient Ascent if you want maximums) where you step-by-step approach an extremum by stepping in the" [YouTube Link](https://youtube.com/watch?v=fXQXE96r4AY) 2023-02-14T17:02Z 580K followers, 106.7K engagements "Weird notions of "distance" Intro to Metric Spaces Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free and the first [---] people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations https://www.beautifulequation.com/pages/trefor Weird funky types of distance can still be thought of as "distance" but what actually is distance anyways In this video we are going to introduce the big ideas of Metric Spaces. A Metric Space tries to generalize the notion of distance that we are all familiar with:" [YouTube Link](https://youtube.com/watch?v=fl5fOAYY-1s) 2022-04-11T16:00Z 580K followers, 108.7K engagements "Proof by Contradiction Method & First Example Proof by Contradiction is one of the most important proof methods. It is an indirect proof technique that works like this: You want to show a statement P is true. First assume the P is actually false. Then manipulate until you get a contradiction like 0=1. This means your assumption that P was false is incorrect and so P is true. QED. In this video we'll talk about the structure of proof by contradiction and then do a small example where we prove a theorem that no integer is both even and odd. Full DISCRETE MATH Course Playlist:" [YouTube Link](https://youtube.com/watch?v=huGWXh4l1M0) 2017-06-13T14:30Z 580K followers, 276.7K engagements "Integration in Spherical Coordinates Spherical Coordinates is a new type of coordinate system to express points in three dimensions. It consists of a distance rho from the origin to the point an azimuthal angle phi between this line and the z axis and a radial angle theta which is analogous to the angle in polar coordinates when you project onto the xy plane. In this video we will talk about integrating regions in spherical coordinates. Much like polar the conversion introduces a factor of rho squares sin phi in the integrand. The choice of which coordinate system to use depends on the" [YouTube Link](https://youtube.com/watch?v=jBcNOkwiS6k) 2019-12-15T19:38Z 580K followers, 279.1K engagements "Describing Surfaces Explicitly Implicitly & Parametrically // Vector Calculus How can we describe two-dimensional surfaces even if they are embedded in 3D space Similar to the three ways to describe curves in 2D we can do this explicitly implicitly or parametrically. In the case of parametrically we get TWO parameters and choose them to try and naturally represent symmetries in the space. We specifically focus on the example of the cone and see how we can use cylindrical coordinates as a base to build out a parameterization of this space. 0:00 Intro to Surfaces 1:23 Descriptions of Curves" [YouTube Link](https://youtube.com/watch?v=jZRqCfi5_Uo) 2020-11-23T16:18Z 580K followers, 112.8K engagements "The Gaussian Integral // Solved Using Polar Coordinates The gaussian integral - integrating e(-x2) over all numbers is an extremely important integral in probability statistics and many other fields. However it is challenging to solve using elementary methods from single variable calculus. In this video we will see how we can convert it to multivariable calculus and then use tricks from multivariable calculus - in this case converting to polar coordinates - to solve this single variable integral. The crazy thing is that this integral ends up being in terms of pi and if you didn't know about" [YouTube Link](https://youtube.com/watch?v=mrcRODAx-Vk) 2020-07-26T15:17Z 580K followers, 144.1K engagements "The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus In this video we get to the last major theorem in our playlist on vector calculus: The Divergence Theorem. We've actually already seen the two-dimensional analog when we studied the Divergence or Flux form of Green's Theorem. Now we upgrade to the three-dimensional situation where we have a closed smooth surface and a vector field. The question is to what degree is there outwards flux of the vector field across this surface The divergence theorem allows this global property to be compared to a triple integral over" [YouTube Link](https://youtube.com/watch?v=pY4t-ikhzhU) 2020-12-14T15:44Z 580K followers, 180.9K engagements "Autonomous Equations Equilibrium Solutions and Stability MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Autonomous Differential Equations are ones of the form y'=f(y) that is only the dependent variable shows up on the right side. This means the slope fields aka direction fields look the same for all values of the independent variable t. While these are examples of separable differential equations they allow for a lot of new analysis. We can talk about" [YouTube Link](https://youtube.com/watch?v=pZOmToxx-R8) 2021-03-10T16:47Z 580K followers, 160.8K engagements "Reflexive Symmetric and Transitive Relations on a Set A relation from a set A to itself can be though of as a directed graph. We look at three types of such relations: reflexive symmetric and transitive. A relation is reflexive if every element relates to itself that is has a little look from itself to itself. A relation is symmetric if whenever x relates to y then y relates to x. This looks like every path between x and y has a path back. A relation is transitive if whenever xRy and yRz then xRz (this shorthands is read "x relates to y" and so on). This looks like every two step path has a" [YouTube Link](https://youtube.com/watch?v=q0xN_N7l_Kw) 2017-07-09T03:22Z 580K followers, 418.1K engagements "What is [--] Is [--] a natural number MATHEMATICIANS DISAGREE Get better at math everyday at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription Read the full survey on math conventions from Thomas Lam here: https://cims.nyu.edu/tjl8195/survey/results.html 0:00 Math conventions 0:21 [--] is indeterminate 3:01 00=1 5:29 [--] is a natural number 6:53 1/x is a continuous function 8:15 f(x)=1 is increasing 9:46 3x+1 is linear 11:20 Axiom of Choice 13:03 6/2(1+2) 13:21 Brilliant.org/TreforBazett BECOME A MEMBER: Join:" [YouTube Link](https://youtube.com/watch?v=rBz5k2T7p4A) 2024-11-17T17:25Z 580K followers, 67K engagements "Intro to Markov Chains & Transition Diagrams Markov Chains or Markov Processes are an extremely powerful tool from probability and statistics. They represent a statistical process that happens over and over again where we try to predict the future state of a system. A markov process is one where the probability of the future ONLY depends on the present state and ignores the past entirely. This might seem like a big restriction but what we gain is a lot of power in our computations. We will see how to come up with transition diagram to describe the probabilities of shifting between different" [YouTube Link](https://youtube.com/watch?v=rHdX3ANxofs) 2020-09-07T16:16Z 580K followers, 172.3K engagements "How I Make Presentations Using LaTeX & Beamer Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 If you are doing a presentation that involves lots of mathematics we can leverage our LaTeX skills from earlier in the playlist to be able to quickly make a presentation that lets us display beautiful math equations and graphics all with pretty themes and timing" [YouTube Link](https://youtube.com/watch?v=rx7wwtmFlD8) 2022-08-03T16:00Z 580K followers, 306.7K engagements "How curvy is a curve Intro to Curvature & Circles of Curvature Multi-variable Calculus How curvy is a curve In this video we define and come up with a formula for curvature and see how this relates to unit tangent and unit normal vectors. Finally we describe the circle of curvature. While this is a multivariable calculus topic in reference to vector valued functions the question of curvature of a curve can be asked for any planar curve from single variable calculus as well Full Multivariable Calculus Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd" [YouTube Link](https://youtube.com/watch?v=si6ka6HeUdY) 2019-10-20T16:50Z 580K followers, 119K engagements "Cartesian Product of Two Sets A x B Learning Objectives: 1) Define an ordered pair 2) Define the Cartesian Product of two sets 3) Find all the elements in a Cartesian Product **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS **************************************************** Other Course" [YouTube Link](https://youtube.com/watch?v=ufjEv-5nmcA) 2017-05-05T01:09Z 580K followers, 222.2K engagements "3 Properties of Laplace Transforms: Linearity Existence and Inverses The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions are reasonably nice - something we will call of exponential order - then the Laplace Transform converges. 3) Inverses. For L(f(t)=F(s) there is a unique f(t) for any given F(s). What this means is that we can define an inverse Laplace" [YouTube Link](https://youtube.com/watch?v=zModDQ-ST30) 2020-03-17T18:51Z 580K followers, 190K engagements "Laplace Transform and Piecewise or Discontinuous Functions Watch the Intro to the Laplace Transform in my Differential Equations playlist here: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 This video deals particularly with how the Laplace Transform works with piecewise functions a type of discontinuous functions. The easiest example of which is the step function or heaviside function and we use that example to deal with the more complicated cases. Indeed one of the big advantages of the Laplace Transform is that it deals with discontinuous functions so well" [YouTube Link](https://youtube.com/watch?v=zo4Stc-raQE) 2020-04-25T21:08Z 580K followers, 147.2K engagements "How to write a thesis using LaTeX **full tutorial** Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. My LaTex Videos: PART I: LaTeX for complete beginners : https://www.youtube.com/watchv=Jp0lPj2-DQA PART II: Full LaTeX tutorial: https://www.youtube.com/watchv=-HvRvBjBAvg PART IV: My Favorite Packages: https://www.youtube.com/watchv=331YxgOJUGw In this video I'll talk about all the major things needed to write a thesis using LaTeX a markup language that is great for displaying" [YouTube Link](https://youtube.com/watch?v=zqQM66uAig0) 2021-10-26T16:33Z 580K followers, 917.7K engagements Limited data mode. Full metrics available with subscription: lunarcrush.com/pricing
@drtrefor Dr. Trefor Bazett
Dr. Trefor Bazett posts on YouTube about math, how to, solve, this is the most. They currently have [-------] followers and [---] posts still getting attention that total [------] engagements in the last [--] hours.
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Social Influence
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"How to make your LaTeX documents BEAUTIFUL // LaTeX Tutorial Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 In this video we're covering how to make your LaTeX documents BEAUTIFUL. We starts with columns using twocolumn in the document class the multicol package and using minipages. Next up is margins and margin notes. We talk about white space"
YouTube Link 2023-04-19T18:23Z 580K followers, 135K engagements
"Tables in LaTeX Full Tutorial Intro to LaTeX Episode [--] Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 The file I used in the above video is here: https://www.overleaf.com/read/pjzsxngjqqfp Overleaf's written guide to tables is here: https://www.overleaf.com/learn/latex/Tables This video is all about using tables in LaTeX. I'll show you the basics of the"
YouTube Link 2022-11-21T17:35Z 580K followers, 148.4K engagements
"Intro to VECTOR FIELDS // Sketching by hand & with computers Vector Fields are extremely important in math physics engineering and many other fields. Gravitational fields electric fields magnetic fields velocity fields these are all examples of vector fields. In this video we will define the concept of a vector field talk about some basic terminology practice drawing vector fields by hand and then turn to the technology to plot vector fields on the computer. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa 2D"
YouTube Link 2020-10-11T15:08Z 580K followers, 159.8K engagements
"Proof by Contrapositive Method & First Example Learning objective: prove an implication by showing the contrapositive is true. This video is part of a Discrete Math course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett Mathematics Education University of Cincinnati Discrete Math Proof by Contrapositive Mathematics Education University of Cincinnati Discrete Math Proof by Contrapositive"
YouTube Link 2017-06-13T14:46Z 580K followers, 176.2K engagements
"The Method of Integrating Factors for Linear 1st Order ODEs full example MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs In this video we do a full example using the method of integrating factors to solve a first order differential equation. The first thing to observe is that this is a linear ODE. Then we apply the integral formula to get the integrating factor and finally use that to get a solution to the ODE. ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON:"
YouTube Link 2021-03-01T16:57Z 580K followers, 259K engagements
"3D Curves and their Tangents Intro to Vector-Valued Functions A space curve or vector-valued function is a function with a single input t and multiple outputs x(t) y(t) z(t). In this video we introduce these functions and see how to visualize them in 3D. We then turn to the problem of tangent lines to these types of curves. The definition is modeled after tangents to graphs of functions. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems"
YouTube Link 2019-10-08T00:34Z 580K followers, 157.5K engagements
"All the LOGARITHMS needed for calculus actually explained Self-study with Brilliant at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription In this video we're going to see all the logarithm rules you should know to take a calculus course. We define logarithm as the inverse function to the exponential so if bx=y then log_b y = x. We really like it when the base is e and this gives the natural logarithm. There are a bunch of rules like for products and quotients and powers but for all of these you can figure out the logarithm"
YouTube Link 2025-02-24T17:41Z 580K followers, 34.2K engagements
"Harmonic Series It diverges but insanely slowly After the Geometric Series the Harmonic Series is one of the most important examples in Calculus. This is a series that we will show - by investigating the partial sums - diverges. But it turns out to diverge incredibly slowly taking over [----] terms just to add up to [---]. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: CALCULUS II:"
YouTube Link 2019-02-15T13:44Z 580K followers, 76.5K engagements
"Separation of Variables // Differential Equations MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs In this video we talk about our first major method for solving differential equations: the method of separation of variables. A first order ODE is separable if it can be written as y'=f(t)g(y) that is a product of two factors that each only depend on one of the variables. If that is the case then we can separate and integrate. We're going to see in this video the"
YouTube Link 2021-01-27T17:17Z 580K followers, 206.1K engagements
"Lagrange Multipliers Geometric Meaning & Full Example Lagrange Multipliers solve constrained optimization problems. That is it is a technique for finding maximum or minimum values of a function subject to some constraint like finding the highest point on a mountain subject to the fact you can only walk along a trail. In this video we study the contour lines or level curves of a function and see geometrically why they are maximized when they are tangent to the constraint curve. That tangency condition leads to the algebraic formula that the gradient of f is equal to lambda times the gradient"
YouTube Link 2019-11-27T20:32Z 580K followers, 493.2K engagements
"The Multi-Variable Chain Rule: Derivatives of Compositions Suppose that f(xy) depends on two variables but that the x(t) and y(t) are themselves both functions of t. Then f(x(t) y(t)) is a composition of functions and the derivative of f with respect to t is computed via the multi-variable Chain Rule. In fact this scenario is one of many different generalizations of the single variable chain rule. We can use arrow (or dependency) diagrams to illustrate the relationships between a bunch of multivariable functions and for each situation write down a chain rule that gives the slope. The idea in"
YouTube Link 2019-11-13T17:30Z 580K followers, 146.6K engagements
"What is VECTOR CALCULUS Full Course Introduction MY VECTOR CALCULUS PLAYLIST https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa Welcome to the start of a full course on vector calculus. In this intro video I'm going to give an overview of the major concepts and ideas that we are going to be seeing throughout the course: Vector Fields Line Integrals Surface Integrals Flux & Flow and the big theorems of Green's Theorem Stokes' Theorem and the Divergence Theorem. It's totally ok if everything doesn't click 100% in this first video the goal is to just give the flavour of"
YouTube Link 2020-11-29T16:51Z 580K followers, 406K engagements
"Undetermined Coefficients: Solving non-homogeneous ODEs MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs How can we solve an ordinary differential equation (ODE) like y''-2y'-3y=3e2t. The problem is the non-homogeneity on the right hand side. If this was homogeneous and just zero then previously in our playlist we've studied how to solve constant coefficient homogeneous equations. To deal with the non-homogeneity we use a method called undetermined coefficients."
YouTube Link 2021-04-19T16:10Z 580K followers, 591.5K engagements
"What is a DIFFERENTIAL EQUATION Intro to my full ODE course Free Open-Source ODE Textbook I'm adapting for this playlist: http://web.uvic.ca/tbazett/diffyqs The ODE Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw In this video I'm giving an introduction to ODEs or Ordinary Differential Equations. Our goal is to model a world where properties are changing and we note from Calculus that rates of change were encoded by the derivative of a function. But where did those functions come from Often the answer is differential equations. We're going to see"
YouTube Link 2021-01-13T18:13Z 580K followers, 402.8K engagements
"Visualizing a 4D Sphere ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:"
YouTube Link 2025-11-05T18:26Z 580K followers, 42.2K engagements
"Directional Derivatives What's the slope in any direction A directional derivative gives the slope in any particular direction similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient you can get the directional derivative in the u direction with one easy dot"
YouTube Link 2019-11-17T17:56Z 580K followers, 265.8K engagements
"Computing the Fourier Series of EVEN or ODD Functions full example In this video we do a full example of computing out a Fourier Series for the case of a sawtooth wave. We get to exploit the fact that this is an odd function where f(-x)=-f(x)) as we can simplify considerably our computations of the Fourier Coefficients if the function is either even or odd. Previous videos in the Fourier Series playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hR Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on"
YouTube Link 2021-05-09T15:43Z 580K followers, 201.9K engagements
"Defining Double Integration with Riemann Sums Volume under a Surface We generalize the ideas of integration from single-variable calculus to define double integrals. The big idea in single variable calculus was to chop up the region into a sum of little rectangles called the Riemann sum which was an approximation for the area under a function. Then we took a limit of the Riemann sum to define the definite integral. We do much the same here looking to find a formula for the volume under a surface. Now a rectangular region in the domain is broken up into a lot of little prisms and the sum of"
YouTube Link 2019-12-01T17:33Z 580K followers, 99.7K engagements
"Intro to the Laplace Transform & Three Examples Welcome to a new series on the Laplace Transform. This remarkable tool in mathematics will let us convert differential equations to algebraic equations we can solve and then convert back. In this first video we will define the Laplace Transform as an improper integral. We will see three examples: exponential functions the step function aka Heaviside function and the Laplace Transform of polynomials. The latter examples will make use of something called the Gamma Function and we will see it has nice properties related to factorials. Laplace"
YouTube Link 2020-03-15T19:37Z 580K followers, 1.3M engagements
"Logical Arguments - Modus Ponens & Modus Tollens Modus Ponens and Modus Tollens are two logical argument forms. In either case these have two premises and a conclusion. These argument forms are called valid which means that if you accept the hypotheses then it is valid to conclude the conclusion. This is distinct from having a sound argument which means not only is the structure logically valid but additionally the premises are true. In this video we will learn how to analyze a written argument by its logical structure as well as write out the truth table for Modus Ponens and Modus Tollens."
YouTube Link 2017-05-23T00:47Z 580K followers, 469.8K engagements
"Analyzing an argument for validity Learning Objectives: 1) Analyze an argument to determine it's logical structure 2) Decide if the logical form of an argument is valid or invalid The main argument forms are Modus Ponens Modus Tollens Generalization Specialization and Contradiction. To see more on each of these check out the following playlist: Full DISCRETE MATH Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Other Course Playlists: CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:"
YouTube Link 2017-05-23T17:45Z 580K followers, 142.3K engagements
"A unified view of Vector Calculus (Stoke's Theorem Divergence Theorem & Green's Theorem) In the final video of my vector calculus playlist (congrats to everyone for making it to the end) I want to do a bit of an overview of the major theorems we have seen in this course - Stokes' Theorem Divergence Theorem Green's Theorem - all are part of a unified framework. Loosely integrating a differential operator such as the curl or divergence along a region equates to a quantity computed just along the boundary. Exactly what quantity (flux vs circulation say) changes depending on the set-up but they"
YouTube Link 2020-12-18T16:40Z 580K followers, 155.4K engagements
"The Dirac Delta 'Function': How to model an impulse or infinite spike In this introduction to the Dirac Delta Function we'll see how we can deal with something happening instantaneously like a hammer hit. We will model this impulse with a 'function' that is infinite at one point and zero everywhere else. But such a thing isn't really a function Sometimes we called it a functional or a generalized function. Regardless it is defined by its pleasing properties such as what happens when you integrate the dirac delta function multiplied by another function. It can also be thought of as the"
YouTube Link 2020-05-09T18:31Z 580K followers, 131.9K engagements
"Double Integration in Polar Coordinates Example & Derivation While Cartesian coordinates are great and all some regions and some integrands are way nicer when described using polar coordinates. In this video we play around with polar coordinates derive the formula for double integration in polar coordinates and see an example. The derivation is much like it was in Cartesian coordinates - a limit of a sum of little volumes - but the geometry of the little volumes change in polar coordinates as they no longer have rectangular bases. Full Multivariable Calculus Playlist:"
YouTube Link 2019-12-08T20:14Z 580K followers, 173.3K engagements
"Torsion: How curves twist in space and the TNB or Frenet Frame If you have a curve through space torsion measures the degree to which the curve "twists". This is separate from how the curve "curves" which we saw was given by the curvature formula. In this video we will study the TNB or Frenet Frame given by three vectors the Tangent the principle Normal and the new vector called the BiNormal vector. The Tangent and Normal Vectors define a plane and what Torsion measures is how that plane changes as you move along the curve. TYPO: Near the beginning the Normal Vector should be 1/k dT/ds. I"
YouTube Link 2019-10-23T19:54Z 580K followers, 198.8K engagements
"Bayes' Theorem - The Simplest Case Second Bayes' Theorem example: https://www.youtube.com/watchv=k6Dw0on6NtM Third Bayes' Theorem example: https://www.youtube.com/watchv=HaYbxQC61pw FULL Discrete Math Playlist: https://www.youtube.com/watchv=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(AB) to P(BA). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given"
YouTube Link 2017-11-19T01:32Z 580K followers, 1.9M engagements
"Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Consider a mass on a spring moving horizontally. The only force on the mass is the spring itself which we can model using Hooke's Law. Then by Newton's Second Law that F=ma this gives the differential equation mx''+kx=0. This is a second order constant coefficient homogeneous differential equation which we can study We use our techniques from"
YouTube Link 2021-04-11T16:10Z 580K followers, 101.3K engagements
"Multi-variable Optimization & the Second Derivative Test Finding Maximums and Minimums of multi-variable functions works pretty similar to single variable functions. Firstfind candidates for maximums/minimums by finding critical points. Critical Points are where the partial derivatives with respect to x and y are both zero. Then we classify each critical point using the second derivative test. In the multivariable case there is a new option beyond max/min/neither there is also the case of the saddle point. The second derivative test involves computing the Hessian the determinant of a matrix"
YouTube Link 2019-11-24T17:40Z 580K followers, 143.8K engagements
"Unlocking the secrets of Magic Square puzzles Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription Magic Square puzzles are some of my favourite recreational math puzzles. Fill up a 3x3 square with the numbers [--] through [--] each used once so every row column and main diagonals add up to the same number. More generally it can be a nxn square with numbers [--] through n2 and there are actually tonnes of variants of these. In this video we will prove that there is precisely [--] possible 3x3 magic"
YouTube Link 2023-05-30T15:45Z 580K followers, 70.3K engagements
"Using Laplace Transforms to solve Differential Equations full example How can we use the Laplace Transform to solve an Initial Value Problem (IVP) consisting of an ODE together with initial conditions in this video we do a full walkthrough beginning with the differential equation converting it to an algebraic equation via the Laplace Transform solving that algebraic equation and finally converting back to a solution to the IVP through the Inverse Laplace Transform. This is part of my series on the Laplace Transforms in my Differential Equations Playlist:"
YouTube Link 2020-03-21T23:40Z 580K followers, 380.5K engagements
"What does "equal" actually mean Get better at MATH and Computer Science with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:"
YouTube Link 2025-12-01T18:03Z 580K followers, 83K engagements
"Intro to Conditional Probability What is the probability of an event A given that event B has occurred We call this conditional probability and it is governed by the formula that P(AB) which reads "probability of A given B" is equal to the P(A intersect B)/P(B). We look at an example involving the probability of being an alcoholic given that one is a man. Conditional Probability Formula: P(AB) = P(A and B)/P(B) FULL DISCRETE MATH PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH"
YouTube Link 2017-11-19T00:46Z 580K followers, 1.6M engagements
"How to Compute a FOURIER SERIES // Formulas & Full Example How do you actually compute a Fourier Series In this video I walk through all the big formulas needed to compute the coefficients in a Fourier Series. First we see three integrals that will really make everything easier integrals of products of sin and cos terms of different frequencies. Then we will use these to compute out formulas for the coefficients of the in and cos terms. Next we see a full example computing everything and finally see the formulas for the general situation. Watch the first video in my playlist here:"
YouTube Link 2021-05-06T15:39Z 580K followers, 532.2K engagements
"Finding the scalar potential function for a conservative vector field // Vector Calculus The fundamental theorem of line integrals told us that if we knew a vector field was conservative and thus able to be written as the gradient of a scalar potential function we could evaluate any line integral almost trivially by just evaluating that potential function at the endpoints. But how do we FIND the scalar potential function This video introduces that method. First we test that our vector field really is conservative using the test we saw previously. But after we know the method applies we apply"
YouTube Link 2020-11-16T17:12Z 580K followers, 166K engagements
"Rotation Matrices Linear Algebra Fundamentals Get better at MATH and Computer Science with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription FULL PLAYLIST: LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett 0:00 Rotations"
YouTube Link 2025-11-17T18:43Z 580K followers, 14.1K engagements
"Flux Integrals // Big Idea Formula & Examples // Vector Calculus The Flux along a closed curve measures the degree to which a vector field is crossing outward across the curve. We compute this using a flux integral. In contrast to our previous video discussing flow which represented the degree to which the field was tangential to the curve flux accumulates the degree to which the field is normal to the curve. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa 0:00 Geometric Idea 2:15 Formula 4:40 Derivation 9:06"
YouTube Link 2020-10-28T16:27Z 580K followers, 125.5K engagements
"Change of Variables & The Jacobian Multi-variable Integration You've reached the end of Multi-variable Calculus In this video we generalized the good old "u-subs" of first year calculus to multivariable case with a multivariable change of variables. The trick is to set up a new coordinate system where the messy region before is now very nice perhaps just a rectangle. We have to be careful though as we have to multiply our integrands by a scaling factors called the Jacobian. In this video I sketch the intuition behind the Jacobian and compute it out in an example."
YouTube Link 2019-12-18T20:53Z 580K followers, 421.6K engagements
"The Laplace Transform of Derivatives and Integrals In this video we take the Laplace Transform of derivatives or integrals. What's amazing is that these result in expressions entirely in terms of the original function. This will be important for us when we take the Laplace Transform of a differential equation because it will convert an ODE with initial conditions into an algebraic equation we can hopefully solve more easily. Formulas: 1) Lf(t)=sF(s)-f(0) 2)L integral from [--] to t of f(tau) = F(s)/s This is part of my series on the Laplace Transforms in my Differential Equations Playlist:"
YouTube Link 2020-03-18T21:11Z 580K followers, 193.8K engagements
"Line Integrals of Vector Fields // Big Idea Definition & Formula Previously in the Vector Calculus playlist (see below) we have seen the idea of a Line Integral which was an accumulation of some function along a curve. In this video we're going to look at case where we begin with a vector field and want to measure the accumulation of the field tangential to the curve. A great example of this is the physics concept of work done by a field on a particle moving along a curve. In this video we will define the basic concept of the line integral of a vector field along a curve and then determine a"
YouTube Link 2020-10-14T15:00Z 578K followers, 244.4K engagements
"The beautiful geometric view of FOURIER SERIES // The Linear Algebra Perspective Fourier Series can sometimes seem very computational and full of integrals but there is actually a very deep and important geometric picture that is analogous to Linear Algebra. So many core ideas from linear algebra like bases linear independence orthogonality inner products and projections all have their analogs in Fourier Series. Effectively the idea of computing a Fourier Series is just decomposing a vector in an orthonormal basis. Cool The rest of my Fourier Series Playlist:"
YouTube Link 2021-05-12T15:47Z 579K followers, 80.5K engagements
"Subspaces of Rn Subspaces are those subsets that play nice with the fundamental operations on vectors. That is we say they are "closed under scalar multiplication" and "closed under vector addiction". Examples include everything just the zero vector and lines through the origin. Learning Objectives 1) Define a subspace 2) Determine if a set is a subspace by checking whether it satisfies the three properties. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS &"
YouTube Link 2017-06-11T00:30Z 580K followers, 15.3K engagements
"Vector Spaces Definition & Examples Vectors in Rn obey a list of rules things like commutivity of vector addition that a+b = b+a as vectors. However we can abstract this list of rules and introduce the general concept of a vector space. A vector space has elements that might be all kinds of weird things but as long as they obey the same list of rules they are a vector space. And the key here is that all the things we have done in linear algebra extend to this new situation too Our first new example is polynomial of degree less than or equal [--] which have a natural "vector" addition and scalar"
YouTube Link 2018-06-16T20:27Z 580K followers, 128.9K engagements
"Divergence Flux and Green's Theorem // Vector Calculus In the previous video in our Vector Calculus Playlist (https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa) we saw Part I of Green's Theorem which related the local property of Curl (aka circulation density) with the global property of Circulation. Circulation a line integral over a vector field was compared to a double integral over the area enclosed of the Flux. In this video we look at Part II of Green's Theorem which now contrasts the local property of Divergence (aka Flux Density) with the global property of"
YouTube Link 2020-11-18T16:28Z 579K followers, 105.9K engagements
"The Illusion of Thinking // The new Apple AI paper is.something Get better at MATH with Brilliant at https://brilliant.org/TreforBazett to get started for free and to get 20% off an annual premium subscription Check out: 1) The main Apple paper (and source of all graphs from the video): https://ml-site.cdn-apple.com/papers/the-illusion-of-thinking.pdf 2) Play the Towers of Hanoi game here: https://www.mathsisfun.com/games/towerofhanoi.html ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25%"
YouTube Link 2025-06-11T16:45Z 580K followers, 55.5K engagements
"Stirling's Incredible Approximation // Gamma Functions Gaussians and Laplace's Method We prove Stirling's Formula that approximates n using Laplace's Method. Get my favorite free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Check out MAPLE LEARN for your browser to make beautiful graphs and much more: https://www.maplesoft.com/products/learn/p=TC-9857 Check out Maplesoft's YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ In his video we prove Stirling's Approximation Formula that n"
YouTube Link 2021-11-02T16:34Z 579K followers, 150K engagements
"Normal Form Games // Intro to Game Theory // Episode [--] Check out Brilliant https://brilliant.org/TreforBazett/ Join for free and the first [---] subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video The 1st episode in the Game Theory playlist on the Prisoners Dilemma: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX In this video we introduce our first major category of game that we will study in Game Theory called Normal Form Games. These are games between a finite number of players with each player having a finite"
YouTube Link 2021-07-14T16:19Z 578K followers, 19.5K engagements
"Example: Writing a vector in a new basis Let's work through an explicit example using the change of basis formula from the previous video. Learning Objectives: 1) Given two basis convert a vector expressed in one basis to the other. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A MEMBER: Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett Mathematics Education University of Cincinnati Linear Algebra Change of Basis Mathematics Education"
YouTube Link 2017-06-24T18:46Z 580K followers, 20.2K engagements
"What is a LINE INTEGRAL // Big Idea Derivation & Formula My Vector Calculus playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa A line integral - sometimes called a path integral - is an accumulation of something along a curve (again sometimes called a path). In this first video we will really focus on a curve living in 2D with a height above that curve and answer the question of what is the surface area that results This will be four first major application of line integrals. The plan for this video is to introduce the big idea of line integrals come up with a"
YouTube Link 2020-09-21T16:22Z 580K followers, 352.8K engagements
"Power Series & Intervals of Convergence Power series are series of the form c_n (x-a)n where the c_n is a sequence and x is thought of as a variable. Whether it converges or diverges depends on the x. By applying the Ratio Test we decide the interval upon which the Power Series converges as well as the "ratio of convergence" and the "center" of the power series. The results turn out very analogous to Geometric Series. Full Course Playlist: CALCULUS II: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON:"
YouTube Link 2019-02-28T12:25Z 579K followers, 167.1K engagements
"Intro to Kolmogorov Complexity Typo 1: 25=32 not [--] Just pretend I said "32" throughout the entire video:D Oops. Typo 2: More importantly is that I missed the on the length when talking about randomness at 4:19 and 15:46. That is we say a string y is kolmogorov random aka incompressible if K(y) is greater than or equal to y not just y as written. Kolmogorov Complexity is loosely the shortest computer program that outputs a given string. We'll use this to define a notation of being Kolmogorov random (aka incompressible) and use that to come up with a very nice proof that there are infinitely"
YouTube Link 2025-02-09T17:28Z 580K followers, 42.3K engagements
"Inverse Laplace Transform Example using Partial Fractions In this video in my series on Laplace Transforms we practice compute Inverse Laplace Transforms. In this specific example the rational function isn't of the form where we can use Inverse Laplace Transforms directly so we use Partial Fractions to decompose it into a more straight forward format. Specially this Partial Fraction Decomposition involves repeated linear factors. Finally we use the Laplace Transform table of known functions together with the translation property to compute the final answer. This is part of my series on the"
YouTube Link 2020-04-05T19:29Z 578K followers, 202.3K engagements
"Euler Paths & the [--] Bridges of Konigsberg Graph Theory An Euler Path walks through a graph going from vertex to vertex hitting each edge exactly once. But only some types of graphs have these Euler Paths it depends on the degree of the vertices. We state and motivate the big theorem and then use it to solve the infamous [--] bridges of Konigsberg problem that motivated Euler to start studying graph theory. FULL DISCRETE MATH PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS OTHER COURSE PLAYLISTS: CALCULUS I:"
YouTube Link 2018-12-06T14:34Z 578K followers, 64.3K engagements
"Absolute Convergence vs Conditional Convergence vs Convergence We've seen regular convergence of a series before but now we consider two special cases. Absolute convergence is when we take the series of the absolute value of the terms which gets rid of any possible cancellation like what happened a lot in the Alternating Series Test. Absolute convergence implies regular convergence. Conditional Convergence is when it converges but does not converge absolutely. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you"
YouTube Link 2019-02-22T12:20Z 579K followers, 50.3K engagements
"Did I make a 4D bubble Check out the full length video: https://www.youtube.com/watchv=_ex1z7XBA_M ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE trefor25 for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I:"
YouTube Link 2025-08-04T19:47Z 580K followers, 3.3M engagements
"Deriving the Change-of-Basis formula Description: If I have a vector expressed in one basis we can compute what that vector is expressed in a different basis via the formula derived in this video. Learning Objectives: 1) Write a vector (given in the standard basis) as a matrix times the vector written in a new basis. 2) Write a vector (given in this new basis) as the inverted matrix times the vector written in the standard basis 3) Given a vector in one basis write the vector in some other basis. This video is part of a Linear Algebra course taught at the University of Cincinnati. BECOME A"
YouTube Link 2017-06-24T00:10Z 579K followers, [----] engagements
"Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs While we saw a specific example of Constant Coefficient Homogeneous ODEs in my previous video in the playlist in this video we're going to solve it in generality and really elaborate on the three main cases. The characteristic equation aka auxiliary equation can have either real and distinct root real and repeated roots or complex"
YouTube Link 2021-03-24T16:09Z 578K followers, 103.2K engagements
"Strong Induction // Intro and Full Example Strong Induction is a proof method that is a somewhat more general form of normal induction that let's us widen the set of claims we can prove. Our base case is not a single fact but a list of all the facts up to a particular nth level. Then we demonstrate the (n+1)th level. Previous example: Induction Proofs with inequalities: https://www.youtube.com/watchv=L5iCGi3dW-Y Full DISCRETE MATH Course Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor"
YouTube Link 2017-06-19T21:58Z 580K followers, 296.8K engagements
"Intro to FOURIER SERIES: The Big Idea Welcome to my playlist on Fourier Series. In this first video we explore the big idea of taking a periodic function and approximating it with sin and cos terms of various frequencies. We will define Fourier Series and see what it means for the series to converge to the original function. We'll also see a bit about Gibbs phenomena and what happens around discontinuities. Rest of the videos in this playlist are here: https://www.youtube.com/watchv=wmCIrpLBFds&list=PLHXZ9OQGMqxdhXcPyNciLdpvfmAjS82hR&ab_channel=Dr.TreforBazett ♡♡♡SUPPORT THE CHANNEL♡♡♡"
YouTube Link 2021-05-03T15:50Z 578K followers, 402.5K engagements
"How to solve ODEs with infinite series Intro & Easiest Example: y'=y In this video we see how to find series solutions to solve ordinary differential equations. This is an incredibly powerful tool that really expands the amount of differential equations we can solve. We will first introduce power series and their basic principles along with the standard series expandions for sin(x) cos(x) ex and 1/(1-x) the geometric series. We'll then see how to substitute the series solution into the differential equation manipulate indices and get a recurrence relation on the coefficients. By studying this"
YouTube Link 2020-05-26T16:49Z 578K followers, 102.8K engagements
"Why hyperbolic functions are actually really nice Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription Today we unpack everything to do with hyperbolic functions. In calculus we often see an analytic definition of hyperbolic cosine and hyperbolic sin expressed as exponential functions. But why Analytically this is just asking for the even and odd components of ex. However we can connect this geometrically to hyperbolas and specifically to the area enclosed by a hyperbola. ♡♡♡SUPPORT THE"
YouTube Link 2023-10-30T17:22Z 580K followers, 291K engagements
"Flux of a Vector Field Across a Surface // Vector Calculus in his video we derive the formula for the flux of a vector field across a surface. This is very analogous to our two dimensional story about the flux across a curve. We can describe surfaces either parametrically explicitly or implicitly and so we come up with formula for the flux across a surface for each description. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: DISCRETE MATH:"
YouTube Link 2020-12-08T16:52Z 580K followers, 88.9K engagements
"Conservative Vector Fields // Vector Calculus Many vector fields - such as the gravitational field - have a remarkable property called being a conservative vector field which means that line integrals over that field are path independent. That is if you want to compute a line integral (physically interpreted as work) the ONLY thing that matters is the endpoints not what happens along the field. Cool In this video we define the basic idea and compute out an example modelling gravity that shows this is a conservative vector field. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV)"
YouTube Link 2020-11-03T17:42Z 580K followers, 146K engagements
"The Null Space & Column Space of a Matrix Algebraically & Geometrically To every matrix there are two natural subspaces: the Null Space of A and the Column Space of A denoted Null(A) and Col(A). Col(A) is the range or all the vectors "hit" by a transformation. It turns out this is equivalent to the span of the columns of A. Null(A) is all the vectors in the domain that are sent to zero by the transformation. We visualize these two subspaces prove they actually are subspaces and show how to compute them. ************************************************** Now it's your turn: 1) Summarize the"
YouTube Link 2018-06-16T19:27Z 580K followers, 104.2K engagements
"The Bernoulli Equation // Substitutions in Differential Equations MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs The Bernoulli Equation is a fascinating ODE. On the surface it is a non-linear first order ODE which means we can't use the methods we have developed for first order linear differential equations. However with a substitution u=y(1-n) this converts into a linear ODE and then we can use the method of integrating factors. There are a lot of little"
YouTube Link 2021-03-08T15:49Z 580K followers, 235K engagements
"What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( // Banach Fixed Point Theorem This weird expression of taking cos over and over again is just a sequence x_n=cos(x_n-1). There is a very cool theorem called the Banach Fixed Point Theorem that let's figure out the limit of sequences like this and depends on cos(x) being a so called contractible mapping. 0:00 The sequence 1:17 Cos(x) Graphically 3:25 Spiral Geometric View 7:02 Banach Fixed Point Theorem COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:"
YouTube Link 2022-01-10T17:07Z 580K followers, 749.3K engagements
"The Dimension Theorem Dim(Null(A)) + Dim(Col(A)) = n Also Rank The two canonical subspace of a matrix - the null space and the column space - may seem very different. The null space is in the domain the column space is in the codomain for instance. But they are related by the Dimension Theorem This says that Dim(Null(A)) + Dim(Col(A)) = n. We're going to investigate why this is the case algebraically and geometrically. Along the way we define a new invariant called rank which is just a convenient way to say the number of leading 1s in REF form."
YouTube Link 2018-06-24T13:07Z 580K followers, 47.2K engagements
"How to find the TANGENT PLANE Linear approximation of multi-variable functions How do you find the equation of a tangent plane to the graph of a function f(xy) This is the multi-variable analog of finding the equation of a tangent line to the single variable function f(x). At each point (if f is differentiable) the tangent plane is a linear approximation. To compute this we use the vector equation of a plane with respect to the normal vector. The components of the normal vector come from the partial derivatives so if you can find partial derivatives you can write down the equation of the"
YouTube Link 2019-11-20T01:36Z 580K followers, 189.1K engagements
"9 tips to help you PROVE MATH THEOREMS How can you prove math theorems How do you begin What are the types of logical arguments you can use How do you get unstuck when you don't know what to do In this video i'm going to walk through a series of tips and tricks to help you prove mathematical theorems. We'll talk about the logical structure and contrast proof methods like direct contrapositive contradiction and counterexample. I'll give you concrete template to work from assumptions definitions of assumptions manipulations definition of conclusion and finally the conclusion. And then i'll talk"
YouTube Link 2020-07-05T18:50Z 580K followers, 162K engagements
"Intro to LaTeX Full Tutorial Part II (Equations Tables Figures Theorems Macros and more) Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Part I of my tutorial on LaTeX is here: https://www.youtube.com/watchv=Jp0lPj2-DQA The rest of my LaTeX playlist is here: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link):"
YouTube Link 2021-08-10T16:06Z 580K followers, 305.9K engagements
"Cantor's Diagonal Argument: The rationals and reals have different sizes Cool Math Episode 1: https://www.youtube.com/watchv=WQWkG9cQ8NQ In the first episode we saw that the integers and rationals (numbers like 3/5) have the same "size" - that is there is a bijective function so that you can line up the integers and rationals even though they are infinite sets and even though the rationals has elements like 3/5 that aren't in the integers. In this episode we now compare the integers and the REAL numbers. Using Cantor's Diagonalization Argument we attempt to list all the real numbers - that is"
YouTube Link 2018-04-10T15:37Z 580K followers, 118.9K engagements
"Relations between two sets Definition + First Examples Learning Objectives: 1) Recognize "less than" as an example of a relation 2) Draw a visual picture of a relation 3) State the formal definition of a relation **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS"
YouTube Link 2017-05-05T04:14Z 580K followers, 149.3K engagements
"The Mobius Strip Bubble ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:"
YouTube Link 2025-09-07T15:27Z 580K followers, 253.3K engagements
"Choosing Which Convergence Test to Apply to [--] Series Deciding which convergence test to apply to a given series is often the hardest part of the unit on series convergence. In this video I'm going to loosely walk through some larger strategies for picking and choosing the method focusing on [--] different series and [--] different methods: 0:00 Intro 0:38 Geometric Series 1:30 Integral Test 2:52 Alternating Series Test 3:54 Divergence Test 5:08 Comparison Test 6:46 Limit Comparison Test 7:58 Root Test 8:52 Ratio Test ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH"
YouTube Link 2019-02-25T12:31Z 580K followers, 655.9K engagements
"My favorite LaTeX packages for writing beautiful math documents Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out my LaTeX playlist from complete beginner to expert: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 Check out the specific Overleaf document from this video: https://www.overleaf.com/read/cmprhhrbxrgv#0368fe 0:00 Intro to LaTeX 1:15 Sharing in Overleaf 2:20 Links and urls with hyperref 6:06 Code and quotes with fancyvrb 8:40 Headers"
YouTube Link 2021-11-16T17:31Z 580K followers, 240.1K engagements
"How I make beautiful GRAPHS and PLOTS using LaTeX Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 I make most of my graph and plots inside of LaTeX using a package called pgfplots. LaTeX is a type setting language and I like using it for graphs specifically because I can control all aspects of my graphs very precisely with formatting native and easily"
YouTube Link 2022-05-30T16:35Z 580K followers, 584.4K engagements
"Continuity vs Partial Derivatives vs Differentiability My Favorite Multivariable Function In single variable calculus a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus you might expect a similar relationship with partial derivatives and continuity but it turns out this is not the case In this example what I call the cross function we will see that both partial derivatives exist but that the function is nonetheless not continuous. This means our work is still cut out for us: we need to define a"
YouTube Link 2020-06-14T17:31Z 580K followers, 91.7K engagements
"3 Ways to Show a Logical Equivalence Ex: DeMorgan's Laws DeMorgan's Laws are two important logical equivalences. In introducing these laws I talk about three different ways by which you can demonstrate a logical equivalences: There are truth tables citing known laws and testing for reasonableness. Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett CURIOSITY BOX:"
YouTube Link 2019-01-23T12:55Z 580K followers, 240.9K engagements
"The Key Definitions of Differential Equations: ODE order solution initial condition IVP Get the free Maple Calculator for your phonehttps://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Get Maple Learn for your computer https://www.maplesoft.com/products/learn/p=TC-9857 The Differential Equations playlist https://www.youtube.com/watchv=B5IjsTONKkw&list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw&ab_channel=Dr.TreforBazett Free Open Source textbook on ODEs http://web.uvic.ca/tbazett/diffyqs/ In this video I introduce the core concepts and the precise definitions of Differential"
YouTube Link 2021-01-20T18:10Z 580K followers, 147.2K engagements
"The Gradient Vector Field One prominent example of a vector field is the Gradient Vector Field. Given any scalar multivariable function f: Rnto R we can get a corresponding vector field that has a precise geometrical meaning: the vectors point in the direction of maximal increase of the function. MY VECTOR CALCULUS PLAYLIST: VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA:"
YouTube Link 2020-10-11T15:09Z 580K followers, 166.8K engagements
"Dirac's Belt Trick: Why a [--] rotation twists space but a [--] rotation fixes it Visit https://brilliant.org/TreforBazett/ to help you learn STEM topics for free and the first [---] people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations https://www.beautifulequation.com/pages/trefor When you twist your arm or a belt by [---] degrees the hand or endpoint is back to where it started but the rest of your arm or belt is still twisted. But if you do a [---] degree twist you can manage to untwist your arm or belt This is known as Dirac's"
YouTube Link 2022-05-23T15:03Z 580K followers, 74.4K engagements
"Conditional Statements: if p then q Learning Objectives: 1) Interpret sentences as being conditional statements 2) Write the truth table for a conditional in its implication form 3) Use truth tables to see the disjunctive form of a conditional statement as logically equivalent Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use"
YouTube Link 2017-05-17T22:33Z 580K followers, 936.5K engagements
"The best way to stack blocks ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:"
YouTube Link 2025-10-05T17:47Z 580K followers, 355K engagements
"Geometric Series Convergence Derivation and Example The Geometric Series is one of our foundational series. Unlike most series we will se in Calculus where we can determine convergence but not what it actually converges too for the Geometric Series in fact we not only know exactly when it converges but also what it converges too. Full Course Playlist: CALCULUS II: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett"
YouTube Link 2019-02-14T12:42Z 580K followers, 168.8K engagements
"What is a Solution to a Linear System Intro We kick off our course by establishing the core problem of Linear Algebra. This video introduces the algebraic side of Linear Systems (the next will address the geometric side). In particular we will be able to: *Identify when an equation is linear *Define what a system of linear equations is *Verify that a list of values is a solution to a system of linear equations *Use a_ij notation to express generic linear systems *Use the terminology of coefficients constants and variables. Now it's your turn: 1) Summarize the big idea of this video in"
YouTube Link 2018-04-28T18:03Z 580K followers, 123.6K engagements
"Equations of Planes: Vector & Component Forms Multivariable Calculus We will come up with first the vector form of the equation of a plane and then expand to get the component form of the equation of a plane. The formula is based on knowing: 1) A point on the plane 2) A normal vector to the plane Planes are foundational objects in multivariable calculus (for instance the analog of a tangent line for functions of one variable will be a tangent plane for functions in two variable). Full Multivariable Calculus Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd"
YouTube Link 2019-08-25T16:08Z 580K followers, 188.4K engagements
"An infinite block overhang ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support on PATREON: https://patreon.com/DrTrefor CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS LINEAR ALGEBRA: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 CALCULUS I: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m CALCULUS II:"
YouTube Link 2025-09-30T16:14Z 580K followers, 6.6M engagements
"Intro to Linear Programming This optimization technique is so cool Get Maple Learn https://www.maplesoft.com/products/learn/p=TC-9857 Get the free Maple Calculator for your phonehttps://www.maplesoft.com/products/maplecalculator/download.aspxp=TC-9857 Play around with the exact Maple Learn document I use in the video https://learn.maplesoft.com/#/docId=5586126131167232&key=4B4CFF82514F4F57AC213F59E24CB275B7F3DB27B846486D9CDA0555BD8423CD Play around with the Maple Learn document I use in the video"
YouTube Link 2021-04-06T15:55Z 580K followers, 302.9K engagements
"Change the order of integration to solve tricky integrals The double integral over a region can be expressed in two different ways. It could be that we write dxdy which means that we integrate with respect to x first and then y (called horizontal strip). Or it could be dydx which means y is integrated first and then x (vertical strips). The big idea is we can convert between these and so can choose whichever is the easier of the two. The steps are: 1) Given an integral sketch the region implied by the limits of integration 2) Now interpret that region the opposite way such as vertical strips"
YouTube Link 2020-07-22T15:48Z 580K followers, 289.8K engagements
"Lagrange Multipliers with TWO constraints Multivariable Optimization In our introduction to Lagrange Multipliers we looked at the geometric meaning and saw an example when our goal was to optimize a function (i.e. find maximums and minimums) subject to ONE constraint:https://www.youtube.com/watchv=8mjcnxGMwFo Now we are upgrading to the case of optimizing with two constraints. We will look at how to interpret the lagrange multiplier method geometrically for two constrains and then see a full example. We will also look at the geometry of the special case of optimization function: the distance."
YouTube Link 2020-06-28T18:34Z 580K followers, 94.6K engagements
"Geometric Meaning of the Gradient Vector What direction should you travel to increase your height on a mountain as fast as possible What direction should you travel to keep your height constant (i.e. travel on a contour aka a level curve) In this video we discuss the math of this problem assuming we had some nice function describing the height of the mountain. The gradiant vector whose components are the respective partial derivatives gives us the answer to the direction of maximal increase. Indeed we saw previously how directional derivatives could be written in terms of the gradient vector."
YouTube Link 2020-06-21T15:45Z 580K followers, 282.9K engagements
"How I use AI in LaTeX -- my favorite workflow with Overleaf & Writefull Get started with LaTeX with Overleaf https://www.overleaf.com/registerutm_source=trefor_bazett&utm_medium=youtube&utm_campaign=ol_wf_dec_2022 The AI integrations in this video are made possible due to a collaboration between @overleafeditor and @writefull_ai . My thanks to Overleaf & Writefull for sponsoring today's video FULL LaTeX Playlist https://www.youtube.com/watchv=Jp0lPj2-DQA&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&ab_channel=Dr.TreforBazett 0:00 Intro 1:35 Getting started with LaTeX 3:00 Equations 5:03 Formatting"
YouTube Link 2024-12-02T16:31Z 580K followers, 72.6K engagements
"The Theory of 2nd Order ODEs // Existence & Uniqueness Superposition & Linear Independence MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Previously in our ODE playlist we've studied 1st order differential equations. Now we move to second order differential equations and specifically focus at the beginning on the major theory. What does existence and uniqueness look like for 2nd order linear ODEs We see a remarkable property called superposition and finally we"
YouTube Link 2021-03-18T15:31Z 580K followers, 95K engagements
"What's the big idea of Linear Algebra Course Intro This is the start of a one semester university level course on Linear Algebra that emphasizes both conceptual understanding as well as procedural fluency with the techniques of Linear Algebra. In this video we get to see just the beginning of some of the big ideas of Linear Algebra. FULL PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 Linear Algebra is a story told in two worlds one geometric and one algebraic. The interplay between the two is beautiful and powerful. In this video we introduce the notion"
YouTube Link 2018-02-18T17:24Z 580K followers, 510.4K engagements
"The Big Theorem of Differential Equations: Existence & Uniqueness MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs The theory of differential equations works because of a class of theorems called existence and uniqueness theorems. They tell us given an initial value problem when that IVP has a solution and if a solution exists then it also tells us it is unique. We will focus on the Picard or Picard-Lindelof existence and uniqueness theorem which applies to first"
YouTube Link 2021-02-21T16:33Z 580K followers, 308.8K engagements
"Set-Roster vs Set-Builder notation Learning Objectives: 1) Write a set with infinitely many elements using Set-Roster notation 2) Write a set using Set-Builder notation 3) Convert between these two different notations for sets. **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS"
YouTube Link 2017-04-25T03:17Z 580K followers, 183.2K engagements
"How to write your homework using LaTeX Get the (free) Homework Template https://www.overleaf.com/read/pycnqvvptsvf#94a8a3. This template is on Overleaf my thanks to Overleaf for sponsoring today's video. Overleaf is a cloud-based LaTeX editor that makes it particularly easy (and free) to get started learning LaTeX. The LaTeX full playlist https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 0:00 Intro to LaTeX 1:14 Getting started using Overleaf 2:00 Changing the header 2:58 Basic equations 5:00 Making new problems 7:39 Tables 10:35 Matrices 11:15 Graphics 12:47 Aligned"
YouTube Link 2023-12-05T18:30Z 580K followers, 148K engagements
"All the TRIG you need for calculus actually explained Get better at trig and so much more math at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription This video is all about trigonometry focusing on reviewing everything you are likely to actually use regularly in calculus. Instead of having to memorize a million trig identities I want to show how you can understand trig where the formulas come from and how you can figure them out on your own if you randomly need one in the middle of a test. ♡♡♡SUPPORT THE CHANNEL♡♡♡ Support"
YouTube Link 2024-09-11T16:07Z 580K followers, 387K engagements
"Intro to Gradient Descent Optimizing High-Dimensional Equations Keep exploring at https://brilliant.org/TreforBazett. Get started for free for [--] days and the first [---] people get 20% off an annual premium subscription How can we find maximums and minimums for complicated functions with an enormous number of variables like you might get when studying neural networks or machine learning In this video we are going to talk about a topic from nonlinear optimization called Gradient Descent (or Gradient Ascent if you want maximums) where you step-by-step approach an extremum by stepping in the"
YouTube Link 2023-02-14T17:02Z 580K followers, 106.7K engagements
"Weird notions of "distance" Intro to Metric Spaces Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free and the first [---] people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations https://www.beautifulequation.com/pages/trefor Weird funky types of distance can still be thought of as "distance" but what actually is distance anyways In this video we are going to introduce the big ideas of Metric Spaces. A Metric Space tries to generalize the notion of distance that we are all familiar with:"
YouTube Link 2022-04-11T16:00Z 580K followers, 108.7K engagements
"Proof by Contradiction Method & First Example Proof by Contradiction is one of the most important proof methods. It is an indirect proof technique that works like this: You want to show a statement P is true. First assume the P is actually false. Then manipulate until you get a contradiction like 0=1. This means your assumption that P was false is incorrect and so P is true. QED. In this video we'll talk about the structure of proof by contradiction and then do a small example where we prove a theorem that no integer is both even and odd. Full DISCRETE MATH Course Playlist:"
YouTube Link 2017-06-13T14:30Z 580K followers, 276.7K engagements
"Integration in Spherical Coordinates Spherical Coordinates is a new type of coordinate system to express points in three dimensions. It consists of a distance rho from the origin to the point an azimuthal angle phi between this line and the z axis and a radial angle theta which is analogous to the angle in polar coordinates when you project onto the xy plane. In this video we will talk about integrating regions in spherical coordinates. Much like polar the conversion introduces a factor of rho squares sin phi in the integrand. The choice of which coordinate system to use depends on the"
YouTube Link 2019-12-15T19:38Z 580K followers, 279.1K engagements
"Describing Surfaces Explicitly Implicitly & Parametrically // Vector Calculus How can we describe two-dimensional surfaces even if they are embedded in 3D space Similar to the three ways to describe curves in 2D we can do this explicitly implicitly or parametrically. In the case of parametrically we get TWO parameters and choose them to try and naturally represent symmetries in the space. We specifically focus on the example of the cone and see how we can use cylindrical coordinates as a base to build out a parameterization of this space. 0:00 Intro to Surfaces 1:23 Descriptions of Curves"
YouTube Link 2020-11-23T16:18Z 580K followers, 112.8K engagements
"The Gaussian Integral // Solved Using Polar Coordinates The gaussian integral - integrating e(-x2) over all numbers is an extremely important integral in probability statistics and many other fields. However it is challenging to solve using elementary methods from single variable calculus. In this video we will see how we can convert it to multivariable calculus and then use tricks from multivariable calculus - in this case converting to polar coordinates - to solve this single variable integral. The crazy thing is that this integral ends up being in terms of pi and if you didn't know about"
YouTube Link 2020-07-26T15:17Z 580K followers, 144.1K engagements
"The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus In this video we get to the last major theorem in our playlist on vector calculus: The Divergence Theorem. We've actually already seen the two-dimensional analog when we studied the Divergence or Flux form of Green's Theorem. Now we upgrade to the three-dimensional situation where we have a closed smooth surface and a vector field. The question is to what degree is there outwards flux of the vector field across this surface The divergence theorem allows this global property to be compared to a triple integral over"
YouTube Link 2020-12-14T15:44Z 580K followers, 180.9K engagements
"Autonomous Equations Equilibrium Solutions and Stability MY DIFFERENTIAL EQUATIONS PLAYLIST: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: http://web.uvic.ca/tbazett/diffyqs Autonomous Differential Equations are ones of the form y'=f(y) that is only the dependent variable shows up on the right side. This means the slope fields aka direction fields look the same for all values of the independent variable t. While these are examples of separable differential equations they allow for a lot of new analysis. We can talk about"
YouTube Link 2021-03-10T16:47Z 580K followers, 160.8K engagements
"Reflexive Symmetric and Transitive Relations on a Set A relation from a set A to itself can be though of as a directed graph. We look at three types of such relations: reflexive symmetric and transitive. A relation is reflexive if every element relates to itself that is has a little look from itself to itself. A relation is symmetric if whenever x relates to y then y relates to x. This looks like every path between x and y has a path back. A relation is transitive if whenever xRy and yRz then xRz (this shorthands is read "x relates to y" and so on). This looks like every two step path has a"
YouTube Link 2017-07-09T03:22Z 580K followers, 418.1K engagements
"What is [--] Is [--] a natural number MATHEMATICIANS DISAGREE Get better at math everyday at https://brilliant.org/TreforBazett to get started for free for [--] days and to get 20% off an annual premium subscription Read the full survey on math conventions from Thomas Lam here: https://cims.nyu.edu/tjl8195/survey/results.html 0:00 Math conventions 0:21 [--] is indeterminate 3:01 00=1 5:29 [--] is a natural number 6:53 1/x is a continuous function 8:15 f(x)=1 is increasing 9:46 3x+1 is linear 11:20 Axiom of Choice 13:03 6/2(1+2) 13:21 Brilliant.org/TreforBazett BECOME A MEMBER: Join:"
YouTube Link 2024-11-17T17:25Z 580K followers, 67K engagements
"Intro to Markov Chains & Transition Diagrams Markov Chains or Markov Processes are an extremely powerful tool from probability and statistics. They represent a statistical process that happens over and over again where we try to predict the future state of a system. A markov process is one where the probability of the future ONLY depends on the present state and ignores the past entirely. This might seem like a big restriction but what we gain is a lot of power in our computations. We will see how to come up with transition diagram to describe the probabilities of shifting between different"
YouTube Link 2020-09-07T16:16Z 580K followers, 172.3K engagements
"How I Make Presentations Using LaTeX & Beamer Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. Check out the previous videos in my LaTeX playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73 If you are doing a presentation that involves lots of mathematics we can leverage our LaTeX skills from earlier in the playlist to be able to quickly make a presentation that lets us display beautiful math equations and graphics all with pretty themes and timing"
YouTube Link 2022-08-03T16:00Z 580K followers, 306.7K engagements
"How curvy is a curve Intro to Curvature & Circles of Curvature Multi-variable Calculus How curvy is a curve In this video we define and come up with a formula for curvature and see how this relates to unit tangent and unit normal vectors. Finally we describe the circle of curvature. While this is a multivariable calculus topic in reference to vector valued functions the question of curvature of a curve can be asked for any planar curve from single variable calculus as well Full Multivariable Calculus Playlist: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd"
YouTube Link 2019-10-20T16:50Z 580K followers, 119K engagements
"Cartesian Product of Two Sets A x B Learning Objectives: 1) Define an ordered pair 2) Define the Cartesian Product of two sets 3) Find all the elements in a Cartesian Product **************************************************** YOUR TURN Learning math requires more than just watching videos so make sure you reflect ask questions and do lots of practice problems **************************************************** Full Course Playlist: DISCRETE MATH: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS **************************************************** Other Course"
YouTube Link 2017-05-05T01:09Z 580K followers, 222.2K engagements
"3 Properties of Laplace Transforms: Linearity Existence and Inverses The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions are reasonably nice - something we will call of exponential order - then the Laplace Transform converges. 3) Inverses. For L(f(t)=F(s) there is a unique f(t) for any given F(s). What this means is that we can define an inverse Laplace"
YouTube Link 2020-03-17T18:51Z 580K followers, 190K engagements
"Laplace Transform and Piecewise or Discontinuous Functions Watch the Intro to the Laplace Transform in my Differential Equations playlist here: https://www.youtube.com/playlistlist=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 This video deals particularly with how the Laplace Transform works with piecewise functions a type of discontinuous functions. The easiest example of which is the step function or heaviside function and we use that example to deal with the more complicated cases. Indeed one of the big advantages of the Laplace Transform is that it deals with discontinuous functions so well"
YouTube Link 2020-04-25T21:08Z 580K followers, 147.2K engagements
"How to write a thesis using LaTeX full tutorial Get started with LaTeX using Overleaf: https://www.overleaf.com/utm_source=yt&utm_medium=link&utm_campaign=im22tb. My thanks to Overleaf for sponsoring today's video. My LaTex Videos: PART I: LaTeX for complete beginners : https://www.youtube.com/watchv=Jp0lPj2-DQA PART II: Full LaTeX tutorial: https://www.youtube.com/watchv=-HvRvBjBAvg PART IV: My Favorite Packages: https://www.youtube.com/watchv=331YxgOJUGw In this video I'll talk about all the major things needed to write a thesis using LaTeX a markup language that is great for displaying"
YouTube Link 2021-10-26T16:33Z 580K followers, 917.7K engagements
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